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Birkhäuser

Methods of Fourier Analysis and Approximation Theory

  • Book
  • © 2016

Overview

Editors:
  1. Michael Ruzhansky

    1. Department of Mathematics, Imperial College London, London, United Kingdom

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  2. Sergey Tikhonov

    1. ICREA Research Professor, Centre de Recerca Matemàtica, Barcelona, Spain

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    You can also search for this editor in PubMed   Google Scholar

  • The book disseminates recent progress in Fourier analysis and approximation theory
  • The volume contains contributions in the areas of Fourier analysis, theory of functions, approximation theory, optimisation theory
  • The refereed detailed articles cover a wide spectrum of topics ranging from theory to applications
  • For the benefit of experts and students alike, the volume presents interactions of different aspects within the field, with an extensive introduction containing an overview of modern research in the topics of the book

Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-viii
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  2. Some Problems in Fourier Analysis and Approximation Theory

    • Michael Ruzhansky, Sergey Tikhonov
    Pages 1-19

  4. Function Spaces of Radial Functions

    1. Front Matter

      Pages 113-113
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    2. Elementary Proofs of Embedding Theorems for Potential Spaces of Radial Functions

      • Pablo L. De Nápoli, Irene Drelichman
      Pages 115-138

    3. On Leray’s Formula

      • E. Liflyand, S. Samko
      Pages 139-146

  5. Approximation Theory

    1. Front Matter

      Pages 147-147
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    2. Order of Approximation of Besov Classes in the Metric of Anisotropic Lorentz Spaces

      • K. A. Bekmaganbetov
      Pages 149-159

    3. Analogues of Ulyanov Inequalities for Mixed Moduli of Smoothness

      • M. K. Potapov, B. V. Simonov
      Pages 161-179

    4. Reconstruction Operator of Functions from the Sobolev Space

      • N. T. Tleukhanova
      Pages 181-191
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Keywords

About this book

Different facets of interplay between harmonic analysis and approximation theory are covered in this volume.  The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca  Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

Editors and Affiliations

  • Department of Mathematics, Imperial College London, London, United Kingdom

    Michael Ruzhansky

  • ICREA Research Professor, Centre de Recerca Matemàtica, Barcelona, Spain

    Sergey Tikhonov

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