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Methods of Fourier analysis and approximation theory / Michael Ruzhansky, Sergey Tikhonov, editors.

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 article...

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Bibliographic Details
Online Access: Full Text (via Springer)
Other Authors: Ruzhansky, M. (Michael) (Editor), Tikhonov, Sergey, 1976- (Editor)
Format: eBook
Language:English
Published: Switzerland : Birkhäuser, 2016.
Series:Applied and numerical harmonic analysis.
Subjects:
Fourier analysis.
Approximation theory.
Table of Contents:
  • 1. Introduction
  • 2. Fourier analysis
  • 2.1. Parseval frames
  • 2.2. Hyperbolic Hardy classes and logarithmic Bloch spaces
  • 2.3. Logan's and Bohman's extremal problems
  • 2.4. Weighted estimates for the Hilbert transform
  • 2.5. Q-Measures and uniqueness sets for Haar series
  • 2.6. O-diagonal estimates for Calderón-Zygmund operators
  • 3. Function spaces of radial functions
  • 3.1. Potential spaces of radial functions
  • 3.2. On Leray's formula
  • 4. Approximation theory
  • 4.1. Approximation order of Besov classes
  • 4.2. Ulyanov inequalities for moduli of smoothness
  • 4.3. Approximation order of Besov classes
  • 5. Optimization theory and related topics
  • 5.1. The Laplace-Borel transform
  • 5.2. Optimization control problems
  • 2 Michael Ruzhansky and Sergey Tikhonov.-5.3. Optimization control problems for parabolic equation
  • 5.4. Numerical modeling of the linear filtration
  • References.

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