Fourier Integrals in Classical Analysis

Author: Christopher D. Sogge

Publisher: Cambridge University Press

ISBN: 9780521434645

Category: Mathematics

Page: 236

View: 7582

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An advanced monograph concerned with modern treatments of central problems in harmonic analysis.

Classical Fourier Analysis

Author: Loukas Grafakos

Publisher: Springer

ISBN: 1493911945

Category: Mathematics

Page: 638

View: 8827

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The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and improved references.

Fourier Series

Author: G. H. Hardy,W. W. Rogosinski

Publisher: Courier Corporation

ISBN: 0486316289

Category: Mathematics

Page: 112

View: 6544

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Classic graduate-level text discusses the Fourier series in Hilbert space, examines further properties of trigonometrical Fourier series, and concludes with a detailed look at the applications of previously outlined theorems. 1956 edition.

Fourier Analysis

Author: T. W. Körner

Publisher: Cambridge University Press

ISBN: 9780521389914

Category: Mathematics

Page: 591

View: 3856

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The author has provided a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy, and electrical engineering. Each application is placed in perspective with a short essay. The prerequisites are few (the reader with knowledge of second or third year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining.

An Introduction to Harmonic Analysis

Author: Yitzhak Katznelson

Publisher: Cambridge University Press

ISBN: 9780521543590

Category: Mathematics

Page: 314

View: 8786

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First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.

The Fourier Integral and Certain of Its Applications

Author: Norbert Wiener

Publisher: CUP Archive

ISBN: 9780521358842

Category: Mathematics

Page: 201

View: 4726

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The book was written from lectures given at the University of Cambridge and maintains throughout a high level of rigour whilst remaining a highly readable and lucid account. Topics covered include the Planchard theory of the existence of Fourier transforms of a function of L2 and Tauberian theorems. The influence of G. H. Hardy is apparent from the presence of an application of the theory to the prime number theorems of Hadamard and de la Vallee Poussin. Both pure and applied mathematicians will welcome the reissue of this classic work. For this reissue, Professor Kahane's Foreword briefly describes the genesis of Wiener's work and its later significance to harmonic analysis and Brownian motion.

Semiclassical Analysis

Author: Maciej Zworski

Publisher: American Mathematical Soc.

ISBN: 0821883208

Category: Mathematics

Page: 431

View: 6820

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This book is an excellent, comprehensive introduction to semiclassical analysis. I believe it will become a standard reference for the subject. --Alejandro Uribe, University of Michigan Semiclassical analysis provides PDE techniques based on the classical-quantum (particle-wave) correspondence. These techniques include such well-known tools as geometric optics and the Wentzel-Kramers-Brillouin approximation. Examples of problems studied in this subject are high energy eigenvalue asymptotics and effective dynamics for solutions of evolution equations. From the mathematical point of view, semiclassical analysis is a branch of microlocal analysis which, broadly speaking, applies harmonic analysis and symplectic geometry to the study of linear and nonlinear PDE. The book is intended to be a graduate level text introducing readers to semiclassical and microlocal methods in PDE. It is augmented in later chapters with many specialized advanced topics which provide a link to current research literature.

Introduction to Model Spaces and their Operators

Author: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

Publisher: Cambridge University Press

ISBN: 1107108748

Category: Mathematics

Page: 335

View: 3394

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A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.

Automorphic Forms on SL2 (R)

Author: Armand Borel

Publisher: Cambridge University Press

ISBN: 9780521580496

Category: Mathematics

Page: 192

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An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.

NIST Handbook of Mathematical Functions

Author: Frank W. J. Olver

Publisher: Cambridge University Press

ISBN: 0521192250

Category: Mathematics

Page: 951

View: 7726

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The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.

Classical and Modern Fourier Analysis

Author: Loukas Grafakos

Publisher: Prentice Hall

ISBN: N.A

Category: Mathematics

Page: 931

View: 8648

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For graduate-level courses in Fourier or harmonic analysis. Designed specifically for students (rather than researchers), this introduction to Fourier Analysis starts where the real and complex first-year graduate classes end.

Geometric Wave Equations

Author: Jalal M. Ihsan Shatah,Michael Struwe

Publisher: American Mathematical Soc.

ISBN: 0821827499

Category: Mathematics

Page: 137

View: 4457

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This volume contains notes of the lectures given at the Courant Institute and a DMV-Seminar at Oberwolfach. The focus is on the work of the authors on semilinear wave equations with critical Sobolev exponents and on wave maps in two space dimensions. Background material and references have been added to make the notes self-contained. The book is suitable for use in a graduate-level course on the topic. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Number Theory, Fourier Analysis and Geometric Discrepancy

Author: Giancarlo Travaglini

Publisher: Cambridge University Press

ISBN: 1107044030

Category: Mathematics

Page: 252

View: 1074

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"The first part of this book is dedicated to the first goal. The reader will find some topics typically presented in introductory books on Number Theory: factorization, arithmetic functions and integer points, congruences and cryptography, quadratic reciprocity, and sums of two and four squares. Starting from the first few pages we introduce some simple and captivating findings, such as Chebyshev's theorem and the elementary results for the Gauss circle problem and for the Dirichlet divisor problem, which may lead the reader to a deeper study of Number Theory, particularly students who are interested in Calculus and Analysis"--

Classical and Multilinear Harmonic Analysis

Author: Camil Muscalu,Wilhelm Schlag

Publisher: Cambridge University Press

ISBN: 1107031826

Category: Mathematics

Page: 339

View: 3112

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This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

Discourse on Fourier Series

Author: Cornelius Lanczos

Publisher: SIAM

ISBN: 1611974526

Category: Mathematics

Page: 255

View: 3871

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Originally published in 1966, this well-written and still-cited text covers Fourier analysis, a foundation of science and engineering. Many modern textbooks are filled with specialized terms and equations that may be confusing, but this book uses a friendly, conversational tone to clarify the material and engage the reader. The author meticulously develops the topic and uses 161 problems integrated into the text to walk the student down the simplest path to a solution. Intended for students of engineering, physics, and mathematics at both advanced undergraduate and graduate levels.