Methods of Fourier Analysis and Approximation Theory

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

3. Fourier Analysis

   1. Front Matter

      Pages 21-21

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   2. Parseval Frames with n + 1 Vectors in \(\mathbb{R}^{n}\)

      • Laura De Carli, Zhongyuan Hu

      Pages 23-32

   3. Hyperbolic Hardy Classes and Logarithmic Bloch Spaces

      • Evgueni Doubtsov

      Pages 33-42

   4. Multidimensional Extremal Logan’s and Bohman’s Problems

      • D. V. Gorbachev

      Pages 43-58

   5. Weighted Estimates for the Discrete Hilbert Transform

      • E. Liflyand

      Pages 59-69

   6. Q-Measures on the Dyadic Group and Uniqueness Sets for Haar Series

      • Mikhail G. Plotnikov

      Pages 71-83

   7. Off-Diagonal and Pointwise Estimates for Compact Calderón-Zygmund Operators

      • Paco Villarroya

      Pages 85-112

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

6. Optimization Theory and Related Topics

   1. Front Matter

      Pages 193-193

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   2. Laplace–Borel Transformation of Functions Holomorphic in the Torus and Equivalent to Entire Functions

      • L. S. Maergoiz

      Pages 195-209

   3. Optimization Control Problems for Systems Described by Elliptic Variational Inequalities with State Constraints

      • Simon Serovajsky

      Pages 211-224

   4. Two Approximation Methods of the Functional Gradient for a Distributed Optimization Control Problem

      • Ilyas Shakenov

      Pages 225-235

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 9^th 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.

• Fourier Analysis
• Harmonic Analysis
• Approximation Theory
• Optimization Theory
• Function spaces

• 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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