Author:
Publisher: Academic Press
ISBN: 0080874428
Category : Mathematics
Languages : en
Pages : 475

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Book Description
Real-variable Methods in Harmonic Analysis

Author: Alberto Torchinsky
Publisher: Elsevier
ISBN: 1483268888
Category : Mathematics
Languages : en
Pages : 475

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Book Description
Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.

Author: Elias M. Stein
Publisher: Princeton University Press
ISBN: 140088392X
Category : Mathematics
Languages : en
Pages : 711

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Book Description
This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

Author:
Publisher: Elsevier
ISBN: 0080871577
Category : Mathematics
Languages : en
Pages : 407

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Book Description
Real Variable Methods in Fourier Analysis

Author: Yitzhak Katznelson
Publisher:
ISBN:
Category : Harmonic analysis
Languages : en
Pages : 292

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Book Description

Author: Camil Muscalu
Publisher: Cambridge University Press
ISBN: 0521882451
Category : Mathematics
Languages : en
Pages : 389

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

Author: Camil Muscalu
Publisher: Cambridge University Press
ISBN: 1107031826
Category : Mathematics
Languages : en
Pages : 341

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

Author: Alexey N. Karapetyants
Publisher: Springer Nature
ISBN: 3030774937
Category : Mathematics
Languages : en
Pages : 585

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Book Description
This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.

Author: Elias M. Stein
Publisher: Princeton University Press
ISBN: 9780691032160
Category : Mathematics
Languages : en
Pages : 720

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Book Description
This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

Author: Anton Deitmar
Publisher: Springer Science & Business Media
ISBN: 147573834X
Category : Mathematics
Languages : en
Pages : 154

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Book Description
This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.