Format:
1 Online-Ressource (X, 476 Seiten)
ISBN:
9783110265118
Series Statement:
De Gruyter studies in nonlinear analysis and applications volume 17
Content:
Biographical note: Jürgen Appell, University of Würzburg, Germany; Jozef Banas, Technical University of Rzeszow, Poland; Nelson José Merentes Díaz, Central University of Venezuela, Caracas,Venezuela.
Content:
This monographis a self-contained exposition of the definition and properties of functionsof bounded variation and their various generalizations; the analyticalproperties of nonlinear composition operators in spaces of such functions;applications to Fourier analysis, nonlinear integral equations, andboundary value problems.It is written for non-specialists and gives a readable overall acount of the theory, methods, and applications. The bookis written for non-specialists and gives a readable overall acount of the theory, methods, and applications. Every chapter closes with a list of exercises and open problems. Thusthe book serves as a fruitful sourcefor further research.
Note:
Description based upon print version of record
,
Preface; Introduction; 0 Prerequisites; 0.1 The Lebesgue integral; 0.2 Some functional analysis; 0.3 Basic function spaces; 0.4 Comments on Chapter 0; 0.5 Exercises to Chapter 0; 1 Classical BV-spaces; 1.1 Functions of bounded variation; 1.2 Bounded variation and continuity; 1.3 Functions of bounded Wiener variation; 1.4 Functions of several variables; 1.5 Comments on Chapter 1; 1.6 Exercises to Chapter 1; 2 Nonclassical BV-spaces; 2.1 The Wiener-Young variation; 2.2 The Waterman variation; 2.3 The Schramm variation; 2.4 The Riesz-Medvedev variation; 2.5 The Korenblum variation
,
2.6 Higher order Wiener-type variations2.7 Comments on Chapter 2; 2.8 Exercises to Chapter 2; 3 Absolutely continuous functions; 3.1 Continuity and absolute continuity; 3.2 The Vitali-Banach-Zaretskij theorem; 3.3 Reconstructing a function from its derivative; 3.4 Rectifiable functions; 3.5 The Riesz-Medvedev theorem; 3.6 Higher order Riesz-type variations; 3.7 Comments on Chapter 3; 3.8 Exercises to Chapter 3; 4 Riemann-Stieltjes integrals; 4.1 Classical RS-integrals; 4.2 Bounded variation and duality; 4.3 Bounded p-variation and duality; 4.4 Nonclassical RS-integrals
,
4.5 Comments on Chapter 44.6 Exercises to Chapter 4; 5 Nonlinear composition operators; 5.1 The composition operator problem; 5.2 Boundedness and continuity; 5.3 Spaces of differentiable functions; 5.4 Global Lipschitz continuity; 5.5 Local Lipschitz continuity; 5.6 Comments on Chapter 5; 5.7 Exercises to Chapter 5; 6 Nonlinear superposition operators; 6.1 Boundedness and continuity; 6.2 Lipschitz continuity; 6.3 Uniform boundedness and continuity; 6.4 Functions of several variables; 6.5 Comments on Chapter 6; 6.6 Exercises to Chapter 6; 7 Some applications
,
7.1 Convergence criteria for Fourier series7.2 Fourier series and Waterman spaces; 7.3 Applications to nonlinear integral equations; 7.4 Comments on Chapter 7; References; List of functions; List of symbols; Index
,
In English
Additional Edition:
ISBN 9783110265071
Additional Edition:
Erscheint auch als Druck-Ausgabe Appell, Jürgen, 1952 - Bounded variation and around Berlin [u.a.] : De Gruyter, 2014 ISBN 9783110266245
Additional Edition:
ISBN 3110265079
Additional Edition:
ISBN 9783110265071
Language:
English
Subjects:
Mathematics
Keywords:
Funktion von beschränkter Variation
;
Harmonische Analyse
;
Nichtlineare Analysis
;
Funktion von beschränkter Variation
;
Harmonische Analyse
;
Nichtlineare Analysis
;
Electronic books
DOI:
10.1515/9783110265118
URL:
Volltext
(lizenzpflichtig)
Author information:
Appell, Jürgen 1952-
Author information:
Banaś, Józef 1950-
Author information:
Merentes Díaz, Nelson José 1954-
