Elijah Liflyand's Books

Harmonic Analysis on the Real Line

A Path in the Theory

By: Elijah Liflyand

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Harmonic Analysis on the Real Line

A Path in the Theory

By: Elijah Liflyand

This book sketches a path for newcomers into the theory of harmonic analysis on the real line. It presents a collection of both basic, well-known and some less known results that may serve as a background for future research around this topic. Many of these results are also a necessary basis for multivariate extensions. An extensive bibliography, as well as hints to open problems are included. The book can be used as a skeleton for designing certain special courses, but it is also suitable for self-study.

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Page Count

199

Publisher

Springer Nature

Published Date

ISBN 10

3030818926

ISBN 13

9783030818920

Decay of the Fourier Transform

Analytic and Geometric Aspects

By: Alex Iosevich,Elijah Liflyand

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Decay of the Fourier Transform

Analytic and Geometric Aspects

By: Alex Iosevich,Elijah Liflyand

The Plancherel formula says that the L^2 norm of the function is equal to the L^2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L^2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L^2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.

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Page Count

226

Publisher

Springer

Published Date

ISBN 10

3034806256

ISBN 13

9783034806251

Functions of Bounded Variation and Their Fourier Transforms

By: Elijah Liflyand

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Functions of Bounded Variation and Their Fourier Transforms

By: Elijah Liflyand

Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series.

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Page Count

224

Publisher

Springer

Published Date

ISBN 10

3030044297

ISBN 13

9783030044299

Functions of Bounded Variation and Their Fourier Transforms

By: Elijah Liflyand

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Functions of Bounded Variation and Their Fourier Transforms

By: Elijah Liflyand

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Page Count

224

Publisher

Springer

Published Date

ISBN 10

3030044297

ISBN 13

9783030044299

Decay of the Fourier Transform

Analytic and Geometric Aspects

By: Alex Iosevich,Elijah Liflyand

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Decay of the Fourier Transform

Analytic and Geometric Aspects

By: Alex Iosevich,Elijah Liflyand

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Page Count

226

Publisher

Springer

Published Date

ISBN 10

3034806256

ISBN 13

9783034806251

Modern Methods in Operator Theory and Harmonic Analysis

OTHA 2018, Rostov-On-Don, Russia, April 22-27, Selected, Revised and Extended Contributions

By: Alexey Karapetyants

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Modern Methods in Operator Theory and Harmonic Analysis

OTHA 2018, Rostov-On-Don, Russia, April 22-27, Selected, Revised and Extended Contributions

By: Alexey Karapetyants

This proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018. The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis - all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant. Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.

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Page Count

474

Published Date

ISBN 10

3030267490

ISBN 13

9783030267490

Book's by Elijah Liflyand

Harmonic Analysis on the Real Line

Harmonic Analysis on the Real Line

Decay of the Fourier Transform

Decay of the Fourier Transform

Functions of Bounded Variation and Their Fourier Transforms

Functions of Bounded Variation and Their Fourier Transforms

Functions of Bounded Variation and Their Fourier Transforms

Functions of Bounded Variation and Their Fourier Transforms

Decay of the Fourier Transform

Decay of the Fourier Transform

Modern Methods in Operator Theory and Harmonic Analysis

Modern Methods in Operator Theory and Harmonic Analysis

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