Methods of Fourier Analysis and Approximation Theory

• Corporate Author: SpringerLink (Online service)
• Other Authors: Ruzhansky, Michael (Editor), Tikhonov, Sergey (Editor)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
• Edition: 1st ed. 2016.
• Series: Applied and Numerical Harmonic Analysis,
• Subjects: Mathematics.; Harmonic analysis.; Fourier analysis.; Numerical analysis.; Fourier Analysis.; Abstract Harmonic Analysis.; Numerical Analysis.

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...

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. .