# Symmetrization In Analysis

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## Symmetrization in Analysis

Author | : Albert Baernstein II |

Publsiher | : Cambridge University Press |

Total Pages | : 500 |

Release | : 2019-02-28 |

ISBN | : 0521830478 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Symmetrization in Analysis Book Excerpt:**

Develops the modern theory of symmetrization including applications to geometry, PDEs, and real and complex analysis.

## Structural Dynamic Analysis with Generalized Damping Models

Author | : Sondipon Adhikari |

Publsiher | : John Wiley & Sons |

Total Pages | : 384 |

Release | : 2013-11-25 |

ISBN | : 1848215215 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Structural Dynamic Analysis with Generalized Damping Models Book Excerpt:**

Since Lord Rayleigh introduced the idea of viscous damping in his classic work "The Theory of Sound" in 1877, it has become standard practice to use this approach in dynamics, covering a wide range of applications from aerospace to civil engineering. However, in the majority of practical cases this approach is adopted more for mathematical convenience than for modeling the physics of vibration damping. Over the past decade, extensive research has been undertaken on more general "non-viscous" damping models and vibration of non-viscously damped systems. This book, along with a related book Structural Dynamic Analysis with Generalized Damping Models: Identification, is the first comprehensive study to cover vibration problems with general non-viscous damping. The author draws on his considerable research experience to produce a text covering: dynamics of viscously damped systems; non-viscously damped single- and multi-degree of freedom systems; linear systems with non-local and non-viscous damping; reduced computational methods for damped systems; and finally a method for dealing with general asymmetric systems. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications. Contents 1. Introduction to Damping Models and Analysis Methods. 2. Dynamics of Undamped and Viscously Damped Systems. 3. Non-Viscously Damped Single-Degree-of-Freedom Systems. 4. Non-viscously Damped Multiple-Degree-of-Freedom Systems. 5. Linear Systems with General Non-Viscous Damping. 6. Reduced Computational Methods for Damped Systems

## Condenser Capacities and Symmetrization in Geometric Function Theory

Author | : Vladimir N. Dubinin |

Publsiher | : Springer |

Total Pages | : 344 |

Release | : 2014-08-20 |

ISBN | : 3034808437 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Condenser Capacities and Symmetrization in Geometric Function Theory Book Excerpt:**

This is the first systematic presentation of the capacitory approach and symmetrization in the context of complex analysis. The content of the book is original – the main part has not been covered by existing textbooks and monographs. After an introduction to the theory of condenser capacities in the plane, the monotonicity of the capacity under various special transformations (polarization, Gonchar transformation, averaging transformations and others) is established, followed by various types of symmetrization which are one of the main objects of the book. By using symmetrization principles, some metric properties of compact sets are obtained and some extremal decomposition problems are solved. Moreover, the classical and present facts for univalent and multivalent meromorphic functions are proven. This book will be a valuable source for current and future researchers in various branches of complex analysis and potential theory.

## From Analysis to Visualization

Author | : David H. Bailey,Naomi Simone Borwein,Richard P. Brent,Regina S. Burachik,Judy-anne Heather Osborn,Brailey Sims,Qiji J. Zhu |

Publsiher | : Springer Nature |

Total Pages | : 439 |

Release | : 2020-03-16 |

ISBN | : 3030365689 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**From Analysis to Visualization Book Excerpt:**

Students and researchers from all fields of mathematics are invited to read and treasure this special Proceedings. A conference was held 25 –29 September 2017 at Noah’s On the Beach, Newcastle, Australia, to commemorate the life and work of Jonathan M. Borwein, a mathematician extraordinaire whose untimely passing in August 2016 was a sorry loss to mathematics and to so many members of its community, a loss that continues to be keenly felt. A polymath, Jonathan Borwein ranks among the most wide ranging and influential mathematicians of the last 50 years, making significant contributions to an exceptional diversity of areas and substantially expanding the use of the computer as a tool of the research mathematician. The contributions in this commemorative volume probe Dr. Borwein's ongoing legacy in areas where he did some of his most outstanding work: Applied Analysis, Optimization and Convex Functions; Mathematics Education; Financial Mathematics; plus Number Theory, Special Functions and Pi, all tinged by the double prisms of Experimental Mathematics and Visualization, methodologies he championed.

## Plant Toxin Analysis

Author | : Hans F. Linskens,John F. Jackson |

Publsiher | : Springer Science & Business Media |

Total Pages | : 390 |

Release | : 2013-03-09 |

ISBN | : 3662027836 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Plant Toxin Analysis Book Excerpt:**

Chemical defence by means of toxins poisonous to other organisms, be they animals or plants, is widespread amongst the plant kingdom - including microorganisms as well. This book embraces the analysis of a wide range of plant toxins and this fills a gap in the plant pathology and ecological biochemistry fields. The topics covered include toxic extracellular enzymes, host selective toxins, elicitors, phototoxins, aflatoxins, mycotoxins, and ecotoxic substance tests by pollen germination and growth. The analytical procedures, which are used to evaluate the toxins, are covered in such a way that the reader is able to carry them out mostly solely by following the detailed descriptions.

## Models and Methods in Social Network Analysis

Author | : Peter J. Carrington,John Scott,Stanley Wasserman |

Publsiher | : Cambridge University Press |

Total Pages | : 135 |

Release | : 2005-02-07 |

ISBN | : 9781139443432 |

Category | : Social Science |

Language | : EN, FR, DE, ES & NL |

**Models and Methods in Social Network Analysis Book Excerpt:**

Models and Methods in Social Network Analysis, first published in 2005, presents the most important developments in quantitative models and methods for analyzing social network data that have appeared during the 1990s. Intended as a complement to Wasserman and Faust's Social Network Analysis: Methods and Applications, it is a collection of articles by leading methodologists reviewing advances in their particular areas of network methods. Reviewed are advances in network measurement, network sampling, the analysis of centrality, positional analysis or blockmodelling, the analysis of diffusion through networks, the analysis of affiliation or 'two-mode' networks, the theory of random graphs, dependence graphs, exponential families of random graphs, the analysis of longitudinal network data, graphical techniques for exploring network data, and software for the analysis of social networks.

## Continuum Damage Mechanics and Numerical Applications

Author | : Wohua Zhang,Yuanqiang Cai |

Publsiher | : Springer Science & Business Media |

Total Pages | : 1000 |

Release | : 2010-11-19 |

ISBN | : 3642047084 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Continuum Damage Mechanics and Numerical Applications Book Excerpt:**

"Continuum Damage Mechanics and Numerical Applications" presents a systematic development of the theory of Continuum Damage Mechanics and its numerical engineering applications using a unified form of the mathematical formulations in anisotropic and isotropic damage models. The theoretical framework is based on the thermodynamic theory of energy and material dissipation and is described by a set of fundamental formulations of constitutive equations of damaged materials, development equations of the damaged state, and evolution equations of micro-structures. According to concepts of damage-dissipation of the material state and effective evolution of material properties, all these advanced equations, which take nonsymmetrized effects of damage aspects into account, are developed and modified from the traditional general failure models so they are more easily applied and verified in a wide range of engineering practices by experimental testing. Dr. Wohua Zhang is a Professor at Engineering Mechanics Research Center in Zhejiang University of China. Dr. Yuanqiang Cai is a Professor at Department of Civil Engineering in Zhejiang University of China.

## Complex Analysis and Dynamical Systems

Author | : Mark Agranovsky,Anatoly Golberg,Fiana Jacobzon,David Shoikhet,Lawrence Zalcman |

Publsiher | : Birkhäuser |

Total Pages | : 372 |

Release | : 2018-01-31 |

ISBN | : 3319701541 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Complex Analysis and Dynamical Systems Book Excerpt:**

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.

## Making Our Ideas Clear

Author | : Philip Rosenbaum |

Publsiher | : IAP |

Total Pages | : 345 |

Release | : 2015-01-01 |

ISBN | : 1623968690 |

Category | : Psychology |

Language | : EN, FR, DE, ES & NL |

**Making Our Ideas Clear Book Excerpt:**

This book brings pragmatic theory and praxis into dialogue with contemporary psychodynamic ideas, practitioners, and clinical issues. Generally considered as a historical footnote to psychoanalysis, the chapters in this volume demonstrate pragmatism’s continued relevance for contemporary thought. Not only does pragmatism share many of the values and sensibilities of contemporary psychodynamics, its rich philosophical and theoretical emphasis on active meaning making and agentic being in the world complements and extends current thinking about the social nature of self and mind, how we occupy space in the world, non-linear development, and processes of communication.

## Analysis and Topology

Author | : Cabiria Andreian Cazacu,Olli E Lehto,Themistocles M Rassias |

Publsiher | : World Scientific |

Total Pages | : 736 |

Release | : 1998-11-06 |

ISBN | : 9814498599 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Analysis and Topology Book Excerpt:**

The goal of this book is to investigate further the interdisciplinary interaction between Mathematical Analysis and Topology. It provides an attempt to study various approaches in the topological applications and influence to Function Theory, Calculus of Variations, Functional Analysis and Approximation Theory. The volume is dedicated to the memory of S Stoilow. Contents:Brief Summary of My Research Work (S Stoilow)On Stoilow's Work and Its Influence (C A Cazacu & T M Rassias)Contributions to Stoilow's Theory of Riemann Coverings (C A Cazacu)On the Link of Simultaneous Approximations to Vectorially Minimal Projections (A Bacopoulos)Schwarz Problem for Cauchy-Riemann Systems in Several Complex Variables (H Begehr & A Dzhuraev)Generalized Multivalued Variational Inequalities (H Ben-El-Mechaiekh & G Isac)On the Zorn Spaces in Beurling's Approach to the Riemann Hypothesis (H Bercovici & C Foias)Quasi Bounded Excessive Functions and Revuz Measures (L Beznea & N Boboc)Potential Theory on Ordered Sets (N Boboc & Gh Bucur)Cutting and Gluing Back Along a Closed Simple Curve on a Riemann Surface (D Burghelea & C Constantinescu)About Cases of Equality Between the p-Module and the p-Capacity (P Caraman)Some Examples of Dynamical Systems (K Ciesielski)Applications of Controlled Convergence in Analysis (A Cornea)A Generalization of a Theorem of Weierstrass (M Cristea)Conditions D'existence et Propriétés D'une Métrique Conformément Invariante sur les Variétés Riemanniennes Non Compactes (J Ferrand)Barycentric Subdivisions of Partitions with Applications to Higher Dimensional Symbolic Dynamics and Limit Expansions of Homeomorphisms (B Günther)Ricci Curvature, Harnack Functions, and Picard Type Theorems for Quasiregular Mappings (I Holopainen & S Rickman)On Conformal Weldings which Generate Welding Curves of Finite Rotation (A Huber)The Liouville Theorem (T Iwaniec & G Martin)Pseudocontinuous Functions (R A Johnson & W Wilczy(ski)Local Harmonic Analysis for Domains in Rn of Finite Measure (P E T Jorgensen & S Pedersen)Simion Stoilow and the Romanian Mathematical School (M Jurchescu)The Concept of Global Analytic Function and Riemann Surface in Stoilow's Work (M Jurchescu)Pinched 2-Component Kleinian Groups (I Kra & B Maskit)Quasireflections and Holomorphic Functions (S L Krushkal)Der Konforme Modul von Vierecken (R Kühnau)Stoilow's Work in Real Analysis: Its Significance and Its Impact (S Marcus)The Isomorphism Theorem of Kleinian Groups (K Matsuzaki)Topological Results in Analytic Convexity (N Mihalache)Conditions for Differomorphism in the Complex Plane (P T Mocanu)Parametrization of Teichmüller Space by Length Parameters (T Nakanishi & M Näätänen)A Remark on the Integrability and Boundedness of Automorphic Forms (T Ohsawa)Duality for Multiobjective Fractional Programming Problems Involving n-Set Functions (V Preda)Stability and Set-Valued Functions (T M Rassias)Steiner Symmetrization and the Conformal Moduli of Parallelograms (E Reich)Hilbert's Sixteenth Problem (P X Sheng)Non-Existence of Quasimeromorphic Automorphic Mappings (U Srebro)Certain Conjectures and Theorems Involving the Fractional Derivatives of Analytic and Univalent Functions (H M Srivastava)Extremal Teichmüller Mappings with Given Asymptotic Behaviour (K Strebel)Free Quasiconformality in Banach Spaces IV (J Väisälä)Mapping the Disk to Convex Subregions (J A Velling) Readership: Mathematicians and graduate students in mathematics. keywords:Analysis;Topology;Memorial

## Combinatorial Image Analysis

Author | : Reinhard Klette,Jovisa Zunic |

Publsiher | : Springer Science & Business Media |

Total Pages | : 760 |

Release | : 2004-11-22 |

ISBN | : 3540239421 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Combinatorial Image Analysis Book Excerpt:**

This volume presents the proceedings of the 10th International Workshop on Combinatorial Image Analysis, held December 1–3, 2004, in Auckland, New Zealand. Prior meetings took place in Paris (France, 1991), Ube (Japan, 1992), Washington DC (USA, 1994), Lyon (France, 1995), Hiroshima (Japan, 1997), Madras (India, 1999), Caen (France, 2000), Philadelphia (USA, 2001), and - lermo (Italy, 2003). For this workshop we received 86 submitted papers from 23 countries. Each paper was evaluated by at least two independent referees. We selected 55 papers for the conference. Three invited lectures by Vladimir Kovalevsky (Berlin), Akira Nakamura (Hiroshima), and Maurice Nivat (Paris) completed the program. Conference papers are presented in this volume under the following topical part titles: discrete tomography (3 papers), combinatorics and computational models (6), combinatorial algorithms (6), combinatorial mathematics (4), d- ital topology (7), digital geometry (7), approximation of digital sets by curves and surfaces (5), algebraic approaches (5), fuzzy image analysis (2), image s- mentation (6), and matching and recognition (7). These subjects are dealt with in the context of digital image analysis or computer vision.

## Elastic Shape Analysis of Three Dimensional Objects

Author | : Ian H. Jermyn,Sebastian Kurtek,Hamid Laga,Anuj Srivastava |

Publsiher | : Morgan & Claypool Publishers |

Total Pages | : 185 |

Release | : 2017-09-15 |

ISBN | : 1681730286 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Elastic Shape Analysis of Three Dimensional Objects Book Excerpt:**

Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations. We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in R, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this framework is that it is elastic: it performs alignment, registration, and comparison in a single unified framework, while being invariant to shape-preserving transformations. The approach is essentially Riemannian in the following sense. We specify natural mathematical representations of surfaces of interest, and impose Riemannian metrics that are invariant to the actions of the shape-preserving transformations. In particular, they are invariant to reparameterizations of surfaces. While these metrics are too complicated to allow broad usage in practical applications, we introduce a novel representation, termed square-root normal fields (SRNFs), that transform a particular invariant elastic metric into the standard L2 metric. As a result, one can use standard techniques from functional data analysis for registering, comparing, and summarizing shapes. Specifically, this results in: pairwise registration of surfaces; computation of geodesic paths encoding optimal deformations; computation of Karcher means and covariances under the shape metric; tangent Principal Component Analysis (PCA) and extraction of dominant modes of variability; and finally, modeling of shape variability using wrapped normal densities. These ideas are demonstrated using two case studies: the analysis of surfaces denoting human bodies in terms of shape and pose variability; and the clustering and classification of the shapes of subcortical brain structures for use in medical diagnosis. This book develops these ideas without assuming advanced knowledge in differential geometry and statistics. We summarize some basic tools from differential geometry in the appendices, and introduce additional concepts and terminology as needed in the individual chapters.

## Isotope Effects In Chemistry and Biology

Author | : Amnon Kohen,Hans-Heinrich Limbach |

Publsiher | : CRC Press |

Total Pages | : 1096 |

Release | : 2005-11-01 |

ISBN | : 1420028022 |

Category | : Medical |

Language | : EN, FR, DE, ES & NL |

**Isotope Effects In Chemistry and Biology Book Excerpt:**

The field of isotope effects has expanded exponentially in the last decade, and researchers are finding isotopes increasingly useful in their studies. Bringing literature on the subject up to date, Isotope Effects in Chemistry and Biology covers current principles, methods, and a broad range of applications of isotope effects in the physical, biolo

## Fundamentals of Big Data Network Analysis for Research and Industry

Author | : Hyunjoung Lee,Il Sohn |

Publsiher | : John Wiley & Sons |

Total Pages | : 216 |

Release | : 2015-11-16 |

ISBN | : 111901557X |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Fundamentals of Big Data Network Analysis for Research and Industry Book Excerpt:**

Presents the methodology of big data analysis using examples from research and industry There are large amounts of data everywhere, and the ability to pick out crucial information is increasingly important. Contrary to popular belief, not all information is useful; big data network analysis assumes that data is not only large, but also meaningful, and this book focuses on the fundamental techniques required to extract essential information from vast datasets. Featuring case studies drawn largely from the iron and steel industries, this book offers practical guidance which will enable readers to easily understand big data network analysis. Particular attention is paid to the methodology of network analysis, offering information on the method of data collection, on research design and analysis, and on the interpretation of results. A variety of programs including UCINET, NetMiner, R, NodeXL, and Gephi for network analysis are covered in detail. Fundamentals of Big Data Network Analysis for Research and Industry looks at big data from a fresh perspective, and provides a new approach to data analysis. This book: Explains the basic concepts in understanding big data and filtering meaningful data Presents big data analysis within the networking perspective Features methodology applicable to research and industry Describes in detail the social relationship between big data and its implications Provides insight into identifying patterns and relationships between seemingly unrelated big data Fundamentals of Big Data Network Analysis for Research and Industry will prove a valuable resource for analysts, research engineers, industrial engineers, marketing professionals, and any individuals dealing with accumulated large data whose interest is to analyze and identify potential relationships among data sets.

## Encyclopaedia of Mathematics

Author | : Michiel Hazewinkel |

Publsiher | : Springer Science & Business Media |

Total Pages | : 536 |

Release | : 2012-12-06 |

ISBN | : 9401512337 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Encyclopaedia of Mathematics Book Excerpt:**

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

## Proceedings of the Working Conference on Slow neutron Physics 7 12 December 1961

Author | : Obʺedinennyĭ institut i͡adernykh issledovaniĭ (Dubna, Chekhovskiĭ raĭon, R.S.F.S.R.) |

Publsiher | : Unknown |

Total Pages | : 292 |

Release | : 1963 |

ISBN | : 1928374650XXX |

Category | : Neutrons |

Language | : EN, FR, DE, ES & NL |

**Proceedings of the Working Conference on Slow neutron Physics 7 12 December 1961 Book Excerpt:**

## Superconductivity

Author | : Karl-Heinz Bennemann,John B. Ketterson |

Publsiher | : Springer Science & Business Media |

Total Pages | : 1568 |

Release | : 2008-04-25 |

ISBN | : 3540732535 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Superconductivity Book Excerpt:**

This extensive and comprehensive handbook systematically reviews the basic physics, theory and recent advances in superconductivity. Covering the entire field, this unparalleled resource carefully blends theoretical studies with experimental results to provide an indispensable foundation for further research. Leading researchers, including Nobel laureates, describe the state of the art in conventional and unconventional superconductors. In addition to full-coverage of novel materials and underlying mechanisms, the handbook reflects continued, intense research into electron-phone based superconductivity.

## Concentration Inequalities

Author | : Stéphane Boucheron,Gábor Lugosi,Pascal Massart |

Publsiher | : OUP Oxford |

Total Pages | : 496 |

Release | : 2013-02-08 |

ISBN | : 0191655503 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Concentration Inequalities Book Excerpt:**

Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide variety of areas such as machine learning, statistics, discrete mathematics, and high-dimensional geometry. Roughly speaking, if a function of many independent random variables does not depend too much on any of the variables then it is concentrated in the sense that with high probability, it is close to its expected value. This book offers a host of inequalities to illustrate this rich theory in an accessible way by covering the key developments and applications in the field. The authors describe the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented. A self-contained introduction to concentration inequalities, it includes a survey of concentration of sums of independent random variables, variance bounds, the entropy method, and the transportation method. Deep connections with isoperimetric problems are revealed whilst special attention is paid to applications to the supremum of empirical processes. Written by leading experts in the field and containing extensive exercise sections this book will be an invaluable resource for researchers and graduate students in mathematics, theoretical computer science, and engineering.

## Communications in Applied Analysis

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 135 |

Release | : 2000 |

ISBN | : 1928374650XXX |

Category | : Mathematical analysis |

Language | : EN, FR, DE, ES & NL |

**Communications in Applied Analysis Book Excerpt:**

## Essays on Fourier Analysis in Honor of Elias M Stein PMS 42

Author | : Charles Fefferman,Robert Fefferman,Stephen Wainger |

Publsiher | : Princeton University Press |

Total Pages | : 396 |

Release | : 2014-07-14 |

ISBN | : 1400852943 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Essays on Fourier Analysis in Honor of Elias M Stein PMS 42 Book Excerpt:**

This book contains the lectures presented at a conference held at Princeton University in May 1991 in honor of Elias M. Stein's sixtieth birthday. The lectures deal with Fourier analysis and its applications. The contributors to the volume are W. Beckner, A. Boggess, J. Bourgain, A. Carbery, M. Christ, R. R. Coifman, S. Dobyinsky, C. Fefferman, R. Fefferman, Y. Han, D. Jerison, P. W. Jones, C. Kenig, Y. Meyer, A. Nagel, D. H. Phong, J. Vance, S. Wainger, D. Watson, G. Weiss, V. Wickerhauser, and T. H. Wolff. The topics of the lectures are: conformally invariant inequalities, oscillatory integrals, analytic hypoellipticity, wavelets, the work of E. M. Stein, elliptic non-smooth PDE, nodal sets of eigenfunctions, removable sets for Sobolev spaces in the plane, nonlinear dispersive equations, bilinear operators and renormalization, holomorphic functions on wedges, singular Radon and related transforms, Hilbert transforms and maximal functions on curves, Besov and related function spaces on spaces of homogeneous type, and counterexamples with harmonic gradients in Euclidean space. Originally published in 1995. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.