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Bounded Variation and Around.
This monographis a self-contained exposition of the definition and properties of functionsof bounded variation and their various generalizations; the analytical properties of nonlinear composition operators in spaces of such functions; applications to Fourier analysis, nonlinear integral equations,...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
De Gruyter,
[2013]
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| Colección: | De Gruyter series in nonlinear analysis and applications.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Appell, Jürgen, |e author. | |
| 245 | 1 | 0 | |a Bounded Variation and Around. |
| 264 | 1 | |a Berlin : |b De Gruyter, |c [2013] | |
| 264 | 4 | |c ©2013 | |
| 300 | |a 1 online resource (x, 476 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter Series in Nonlinear Analysis and Applications ; |v v. 17 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a This monographis a self-contained exposition of the definition and properties of functionsof bounded variation and their various generalizations; the analytical properties of nonlinear composition operators in spaces of such functions; applications to Fourier analysis, nonlinear integral equations, and boundary value problems. The book is written for non-specialists. Every chapter closes with a list of exercises and open problems. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Functions of bounded variation. | |
| 650 | 6 | |a Fonctions à variation bornée. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Functions of bounded variation |2 fast | |
| 650 | 7 | |a Harmonische Analyse |2 gnd | |
| 650 | 7 | |a Nichtlineare Analysis |2 gnd | |
| 650 | 7 | |a Funktion von beschränkter Variation |2 gnd | |
| 700 | 1 | |a Banas, Jozef, |d 1950- |e author. | |
| 700 | 1 | |a Merentes Díaz, Nelson José, |e author. | |
| 776 | 0 | 8 | |i Print version: |a Appell, Jürgen. |t Bounded Variation and Around. |d Berlin : De Gruyter, ©2013 |z 9783110265071 |
| 830 | 0 | |a De Gruyter series in nonlinear analysis and applications. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=699597 |z Texto completo |
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