Pointwise Variable Anisotropic Function Spaces on ℝⁿ:

Shai Dekel

Published by De Gruyter 2022

Pointwise Variable Anisotropic Function Spaces on ℝⁿ

Shai Dekel

Volume 85 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110761795

Overview
Contents

About this book

Spaces of homogeneous type were introduced as a generalization to the Euclidean space and serve as a suffi cient setting in which one can generalize the classical isotropic Harmonic analysis and function space theory. This setting is sometimes too general, and the theory is limited. Here, we present a set of fl exible ellipsoid covers of ℝn that replace the Euclidean balls and support a generalization of the theory with fewer limitations.

Covers the theory of local approximation using multivariate algebraic polynomials, and anisotropic spaces and representations of functions based on anisotropic multilevel ellipsoid.
Discusses the history of anisotropic functions and applications.

Author information

Shai Dekel, School of Mathematical Sciences, Tel-Aviv University, Israel.

Reviews

Graduate students, researchers in the fields of approximation theory, harmonic analysis and function spaces.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	VII
Contents Publicly Available Download PDF	IX
1 Local polynomial approximation over convex domains in ℝⁿ Requires Authentication Unlicensed Licensed Download PDF	1
2 Anisotropic multilevel ellipsoid covers of ℝⁿ Requires Authentication Unlicensed Licensed Download PDF	37
3 Anisotropic multiresolution analysis Requires Authentication Unlicensed Licensed Download PDF	67
4 Anisotropic wavelets and two-level splits Requires Authentication Unlicensed Licensed Download PDF	85
5 Anisotropic smoothness spaces Requires Authentication Unlicensed Licensed Download PDF	103
6 Anisotropic Hardy spaces Requires Authentication Unlicensed Licensed Download PDF	135
7 Anisotropic singular operators Requires Authentication Unlicensed Licensed Download PDF	217
Bibliography Requires Authentication Unlicensed Licensed Download PDF	233
Index Requires Authentication Unlicensed Licensed Download PDF	237

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate students, researchers in the fields of approximation theory, harmonic analysis and function spaces
Pages
- Front matter: 10
- Main content: 240
Illustrations
- Illustrations: 3
Keywords: Anisotropic spaces; Euclidean space; theory of local approximation; multivariate algebraic polynomials

eBook

Published: April 4, 2022
ISBN: 9783110761795

Hardcover

Published: April 18, 2022
ISBN: 9783110761764