Methods of Fourier Analysis and Approximation Theory

Michael Ruzhansky, Sergey Tikhonov (Herausgeber)

Buch | Softcover

VIII, 258 Seiten

2018 | 1. Softcover reprint of the original 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-80148-3 (ISBN)

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Different facets of interplay between harmonic analysis andapproximation theory are covered in this volume. The topics included areFourier analysis, function spaces, optimization theory, partial differentialequations, and their links to modern developments in the approximation theory.The articles of this collection were originated from two events. The first eventtook place during the 9^th ISAAC Congress in Krakow, Poland, 5th-9th August2013, at the section "ApproximationTheory and Fourier Analysis". The secondevent was the conference on Fourier Analysis and Approximation Theory in theCentre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013,organized by the editors of this volume. All articles selected to be part ofthis collection were carefully reviewed.

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.

Erscheinungsdatum	20.07.2018
Reihe/Serie	Applied and Numerical Harmonic Analysis
Zusatzinfo	VIII, 258 p. 8 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	4102 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Schlagworte	Approximation Theory • fourier analysis • function spaces • Harmonic Analysis • optimization theory
ISBN-10	3-319-80148-1 / 3319801481
ISBN-13	978-3-319-80148-3 / 9783319801483
Zustand	Neuware