Bounded Variation and Around

Jürgen Appell; Józef Banas; Nelson José Merentes Díaz

Published by De Gruyter 2014

Bounded Variation and Around

Jürgen Appell , Józef Banas and Nelson José Merentes Díaz

Volume 17 in the series De Gruyter Series in Nonlinear Analysis and Applications

https://doi.org/10.1515/9783110265118

Overview
Contents

About this book

The aim of this monograph is to give a thorough and self-contained account of functions of (generalized) bounded variation, the methods connected with their study, their relations to other important function classes, and their applications to various problems arising in Fourier analysis and nonlinear analysis.

In the first part the basic facts about spaces of functions of bounded variation and related spaces are collected, the main ideas which are useful in studying their properties are presented, and a comparison of their importance and suitability for applications is provided, with a particular emphasis on illustrative examples and counterexamples. The second part is concerned with (sometimes quite surprising) properties of nonlinear composition and superposition operators in such spaces. Moreover, relations with Riemann-Stieltjes integrals, convergence tests for Fourier series, and applications to nonlinear integral equations are discussed.

The only prerequisite for understanding this book is a modest background in real analysis, functional analysis, and operator theory. It is addressed to non-specialists who want to get an idea of the development of the theory and its applications in the last decades, as well as a glimpse of the diversity of the directions in which current research is moving. Since the authors try to take into account recent results and state several open problems, this book might also be a fruitful source of inspiration for further research.

Author / Editor information

Jürgen Appell, University of Würzburg, Germany; Jozef Banas, Technical University of Rzeszow, Poland; Nelson José Merentes Díaz, Central University of Venezuela, Caracas, Venezuela.

Reviews

"This very interesting and well-written monograph will be useful for students and scientists." Mathematical Reviews

"The book is self-contained and presents a deep description of this class of functions. It can be very useful for beginners in analysis, as well as for experts in certain specific areas. […] The book is very concrete and is a very good combination of deep rigorous results and and detailed explanation. Partly, the book can be included into the educational process and surely will be a table-book for many analysts." Zentralblatt für Mathematik

Supplementary Materials

Contents

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Publicly Available Download PDF	ix
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
0. Prerequisites Requires Authentication Unlicensed Licensed Download PDF	7
1. Classical BV-spaces Requires Authentication Unlicensed Licensed Download PDF	55
2. Nonclassical BV-spaces Requires Authentication Unlicensed Licensed Download PDF	112
3. Absolutely continuous functions Requires Authentication Unlicensed Licensed Download PDF	208
4. Riemann–Stieltjes integrals Requires Authentication Unlicensed Licensed Download PDF	268
5. Nonlinear composition operators Requires Authentication Unlicensed Licensed Download PDF	324
6. Nonlinear superposition operators Requires Authentication Unlicensed Licensed Download PDF	385
7. Some applications Requires Authentication Unlicensed Licensed Download PDF	425
References Requires Authentication Unlicensed Licensed Download PDF	453
List of functions Requires Authentication Unlicensed Licensed Download PDF	467
List of symbols Requires Authentication Unlicensed Licensed Download PDF	468
Index Requires Authentication Unlicensed Licensed Download PDF	472
Backmatter Requires Authentication Unlicensed Licensed Download PDF	477

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate Students, Lecturers, and Researchers who are interested in Function Spaces, Real Analysis, Fourier Analysis, and Nonlinear Analysis; Academic Libraries
Pages
- Front matter: 10
- Main content: 476
Illustrations
- Tables: 41
Keywords: Bounded Variation; Continuity Properties; Monotonicity Properties; Nonlinear Composition Operators; Fourier Analysis; Nonlinear Integral Equation; Boundary Value Problem

eBook

Published: December 12, 2013
ISBN: 9783110265118

Hardcover

Published: December 12, 2013
ISBN: 9783110265071