Introduction To Fourier Analysis On Euclidean Spaces By Em Stein G Weiss
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Author |
: Elias M. Stein |
Publisher |
: Princeton University Press |
Total Pages |
: 318 |
Release |
: 1971-11-21 |
ISBN-10 |
: 069108078X |
ISBN-13 |
: 9780691080789 |
Rating |
: 4/5 (8X Downloads) |
Synopsis Introduction to Fourier Analysis on Euclidean Spaces by : Elias M. Stein
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.
Author |
: Elias M. Stein |
Publisher |
: |
Total Pages |
: |
Release |
: |
ISBN-10 |
: OCLC:844377002 |
ISBN-13 |
: |
Rating |
: 4/5 (02 Downloads) |
Synopsis Introduction to Fourier analysis on Euclidean spaces, by E.M. Stein & G. Weiss by : Elias M. Stein
Author |
: Elías M. Stein |
Publisher |
: |
Total Pages |
: 297 |
Release |
: 1975 |
ISBN-10 |
: OCLC:1025229225 |
ISBN-13 |
: |
Rating |
: 4/5 (25 Downloads) |
Synopsis Introduction to Fourier Analysis on Euclidean Spaces by : Elías M. Stein
Author |
: Elias M. Stein |
Publisher |
: |
Total Pages |
: 310 |
Release |
: 2016 |
ISBN-10 |
: OCLC:1241855515 |
ISBN-13 |
: |
Rating |
: 4/5 (15 Downloads) |
Synopsis Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32 by : Elias M. Stein
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.
Author |
: M. H. Taibleson |
Publisher |
: Princeton University Press |
Total Pages |
: 308 |
Release |
: 2015-03-08 |
ISBN-10 |
: 9781400871339 |
ISBN-13 |
: 1400871336 |
Rating |
: 4/5 (39 Downloads) |
Synopsis Fourier Analysis on Local Fields. (MN-15) by : M. H. Taibleson
This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (real and complex numbers); the rest are local fields (p-adic numbers, p-series fields, and their algebraic extensions). The local fields are studied in an effort to extend knowledge of the reals and complexes as locally compact fields. The author's central aim has been to present the basic facts of Fourier analysis on local fields in an accessible form and in the same spirit as in Zygmund's Trigonometric Series (Cambridge, 1968) and in Introduction to Fourier Analysis on Euclidean Spaces by Stein and Weiss (1971). Originally published in 1975. 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.
Author |
: Charles Fefferman |
Publisher |
: Princeton University Press |
Total Pages |
: 396 |
Release |
: 2014-07-14 |
ISBN-10 |
: 9781400852949 |
ISBN-13 |
: 1400852943 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Essays on Fourier Analysis in Honor of Elias M. Stein (PMS-42) by : Charles Fefferman
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.
Author |
: Elias M. Stein |
Publisher |
: Princeton University Press |
Total Pages |
: 326 |
Release |
: 2011-02-11 |
ISBN-10 |
: 9781400831234 |
ISBN-13 |
: 1400831237 |
Rating |
: 4/5 (34 Downloads) |
Synopsis Fourier Analysis by : Elias M. Stein
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Author |
: Michael Reissig |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 538 |
Release |
: 2005-07-19 |
ISBN-10 |
: 3764372834 |
ISBN-13 |
: 9783764372835 |
Rating |
: 4/5 (34 Downloads) |
Synopsis New Trends in the Theory of Hyperbolic Equations by : Michael Reissig
This book presents several recent developments in the theory of hyperbolic equations. The carefully selected invited and peer-reviewed contributions deal with questions of low regularity, critical growth, ill-posedness, decay estimates for solutions of different non-linear hyperbolic models, and introduce new approaches based on microlocal methods.
Author |
: Mark A. Pinsky |
Publisher |
: American Mathematical Society |
Total Pages |
: 398 |
Release |
: 2023-12-21 |
ISBN-10 |
: 9781470475673 |
ISBN-13 |
: 1470475677 |
Rating |
: 4/5 (73 Downloads) |
Synopsis Introduction to Fourier Analysis and Wavelets by : Mark A. Pinsky
This book provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. Necessary prerequisites to using the text are rudiments of the Lebesgue measure and integration on the real line. It begins with a thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem). Frequently, more than one proof is offered for a given theorem to illustrate the multiplicity of approaches. The second chapter treats the Fourier transform on Euclidean spaces, especially the author's results in the three-dimensional piecewise smooth case, which is distinct from the classical Gibbs–Wilbraham phenomenon of one-dimensional Fourier analysis. The Poisson summation formula treated in Chapter 3 provides an elegant connection between Fourier series on the circle and Fourier transforms on the real line, culminating in Landau's asymptotic formulas for lattice points on a large sphere. Much of modern harmonic analysis is concerned with the behavior of various linear operators on the Lebesgue spaces $L^p(mathbb{R}^n)$. Chapter 4 gives a gentle introduction to these results, using the Riesz–Thorin theorem and the Marcinkiewicz interpolation formula. One of the long-time users of Fourier analysis is probability theory. In Chapter 5 the central limit theorem, iterated log theorem, and Berry–Esseen theorems are developed using the suitable Fourier-analytic tools. The final chapter furnishes a gentle introduction to wavelet theory, depending only on the $L_2$ theory of the Fourier transform (the Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis. The text contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.
Author |
: Steven G. Krantz |
Publisher |
: Springer Nature |
Total Pages |
: 257 |
Release |
: 2023-02-09 |
ISBN-10 |
: 9783031219528 |
ISBN-13 |
: 303121952X |
Rating |
: 4/5 (28 Downloads) |
Synopsis The E. M. Stein Lectures on Hardy Spaces by : Steven G. Krantz
The book The E. M. Stein Lectures on Hardy Spaces is based on a graduate course on real variable Hardy spaces which was given by E.M. Stein at Princeton University in the academic year 1973-1974. Stein, along with C. Fefferman and G. Weiss, pioneered this subject area, removing the theory of Hardy spaces from its traditional dependence on complex variables, and to reveal its real-variable underpinnings. This book is based on Steven G. Krantz’s notes from the course given by Stein. The text builds on Fefferman's theorem that BMO is the dual of the Hardy space. Using maximal functions, singular integrals, and related ideas, Stein offers many new characterizations of the Hardy spaces. The result is a rich tapestry of ideas that develops the theory of singular integrals to a new level. The final chapter describes the major developments since 1974. This monograph is of broad interest to graduate students and researchers in mathematical analysis. Prerequisites for the book include a solid understanding of real variable theory and complex variable theory. A basic knowledge of functional analysis would also be useful.