Ruzhansky M., Tikhonov S. (eds.) Methods of Fourier Analysis and Approximation Theory

Basel: Birkhäuser, 2016. - 255p.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.Some Problems in Fourier Analysis and Approximation TheoryParseval Frames with n + 1 Vectors in \(\mathbb{R}^{n}\)
Hyperbolic Hardy Classes and Logarithmic Bloch Spaces
Multidimensional Extremal Logan’s and Bohman’s Problems
Weighted Estimates for the Discrete Hilbert Transform
Q-Measures on the Dyadic Group and Uniqueness Sets for Haar Series
Off-Diagonal and Pointwise Estimates for Compact Calderón-Zygmund OperatorsElementary Proofs of Embedding Theorems for Potential Spaces of Radial Functions
On Leray’s FormulaOrder of Approximation of Besov Classes in the Metric of Anisotropic Lorentz Spaces
Analogues of Ulyanov Inequalities for Mixed Moduli of Smoothness
Reconstruction Operator of Functions from the Sobolev SpaceLaplace–Borel Transformation of Functions Holomorphic in the Torus and Equivalent to Entire Functions
Optimization Control Problems for Systems Described by Elliptic Variational Inequalities with State Constraints
Two Approximation Methods of the Functional Gradient for a Distributed Optimization Control Problem
Numerical Modeling of the Linear Relaxational Filtration by Monte Carlo Methods