Theory of function spaces

Author(s)

• Triebel, Hans

Bibliographic Information

Theory of function spaces

Hans Triebel

（Monographs in mathematics, v. 78, 84, 100, 107）

Birkhäuser, 1983-2020

• [1]
• 2 : sz
• 2 : us
• 3
• 4

Note

Bibliography: [1], p. 273-283; 2, p. [347]-366; 3, p. 397-416; 4, p. [147]-156

Includes bibliographical references and index

Description and Table of Contents

Volume

4 ISBN 9783030358907

Description

This book is the continuation of the "Theory of Function Spaces" trilogy, published by the same author in this series and now part of classic literature in the area of function spaces. It can be regarded as a supplement to these volumes and as an accompanying book to the textbook by D.D. Haroske and the author "Distributions, Sobolev spaces, elliptic equations".

Table of Contents

Preface.- Fundamental principles.- The essentials, key theorems.- Further topics.- Complements.

Volume

[1] ISBN 9783764313814

Description

The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where - and 0

Table of Contents

Spaces of Entire Analytic Functions.- Function Spaces on Rn.- Function Spaces on Domains.- Regular Elliptic Differential Equations.- Homogeneous Function Spaces.- Ultra-Distributions and Weighted Spaces of Entire Analytic Functions.- Weighted Function Spaces on Rn.- Weighted Function Spaces on Domains and Degenerate Elliptic Differential Equations.- Periodic Function Spaces.- Further Types of Function Spaces.

Volume

2 : sz ISBN 9783764326395

Description

s s T h is b o ok de als w ith the the o ry of func tion s p ac e s of t y p e B and F as it s t ands pq pq at the end of the eigh ties. These t w o scales of spaces co v er man y w ell- kno w n s paces of functions a nd distributions suc h as H.. olde r-Zy gm und s pac e s , Sob ole v s pac e s , fra- tional Sob o lev s paces (prev ious ly a ls o o ft en referred to a s Bes s e l-p o ten tial s paces ), Be s o v s pac e s , i nhom oge ne ous Hardy s p ac e s , s pac e s of BM O-t y p e and l o c al appro - imation s paces whic h are clos ely c onnected with Morrey-Campanato s paces.

Table of Contents

How To Measure Smoothness.- The Spaces and :Definit.- Atoms, Oscillations, and Distinguished Representations.- Key Theorems.- Spaces on Domains.- Mapping Properties of Pseudodifferential Operators.- Spaces on Riemannian Manifolds and Lie Groups.

Volume

3 ISBN 9783764375812

Description

This volume presents the recent theory of function spaces, paying special attention to some recent developments related to neighboring areas such as numerics, signal processing, and fractal analysis. Local building blocks, in particular (non-smooth) atoms, quarks, wavelet bases and wavelet frames are considered in detail and applied to diverse problems, including a local smoothness theory, spaces on Lipschitz domains, and fractal analysis.

Table of Contents

How to Measure Smoothness.- Atoms and Pointwise Multipliers.- Wavelets.- Spaces on Lipschitz Domains, Wavelets and Sampling Numbers.- Anisotropic Function Spaces.- Weighted Function Spaces.- Fractal Analysis: Measures, Characteristics, Operators.- Function Spaces on Quasi-metric Spaces.- Function Spaces on Sets.

by "Nielsen BookData"

Details

• NCID: BA00869120
• ISBN:
  • 3764313811
  • 3764326395
  • 0817626395
  • 3764375817
  • 9783030358907
• LCCN: 82017858
• Country Code: sz
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Basel ; Boston
• Pages/Volumes: 4 v.
• Size: 24 cm
• Classification:
  • LCC : QA403.5
  • DC19 : 515/.2433
  • NDC8 : 413.59
• Subject Headings:
  • LCSH : Fourier analysis
  • LCSH : Function spaces
• Parent Bibliography ID:
  • BA00044892