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 Matem`tica (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.
Front Matter....Pages i-viii
Some Problems in Fourier Analysis and Approximation Theory....Pages 1-19
Front Matter....Pages 21-21
Parseval Frames with n + 1 Vectors in \(\mathbb{R}^{n}\) ....Pages 23-32
Hyperbolic Hardy Classes and Logarithmic Bloch Spaces....Pages 33-42
Multidimensional Extremal Logan’s and Bohman’s Problems....Pages 43-58
Weighted Estimates for the Discrete Hilbert Transform....Pages 59-69
Q-Measures on the Dyadic Group and Uniqueness Sets for Haar Series....Pages 71-83
Off-Diagonal and Pointwise Estimates for Compact Calderón-Zygmund Operators....Pages 85-112
Front Matter....Pages 113-113
Elementary Proofs of Embedding Theorems for Potential Spaces of Radial Functions....Pages 115-138
On Leray’s Formula....Pages 139-146
Front Matter....Pages 147-147
Order of Approximation of Besov Classes in the Metric of Anisotropic Lorentz Spaces....Pages 149-159
Analogues of Ulyanov Inequalities for Mixed Moduli of Smoothness....Pages 161-179
Reconstruction Operator of Functions from the Sobolev Space....Pages 181-191
Front Matter....Pages 193-193
Laplace–Borel Transformation of Functions Holomorphic in the Torus and Equivalent to Entire Functions....Pages 195-209
Optimization Control Problems for Systems Described by Elliptic Variational Inequalities with State Constraints....Pages 211-224
Two Approximation Methods of the Functional Gradient for a Distributed Optimization Control Problem....Pages 225-235
Numerical Modeling of the Linear Relaxational Filtration by Monte Carlo Methods....Pages 237-258
