Verfügbarkeit: Bounded variation and around | Technische Universität München

Bounded variation and around:

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Bibliographische Detailangaben
Beteiligte Personen:	Appell, Jürgen 1952- (VerfasserIn), Banaś, Józef (VerfasserIn), Merentes Díaz, Nelson José 1954- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin De Gruyter 2014
Schriftenreihe:	de Gruyter series in nonlinear analysis and applications 17
Schlagwörter:	Harmonische Analyse Funktion von beschränkter Variation Nichtlineare Analysis
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025157099&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025157099&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	X, 476 S. graph. Darst.
ISBN:	9783110265071 9783110266245

Internformat

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Datensatz im Suchindex

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adam_text	Contents Preface ------ v Introduction ------1 0 Prerequisites -----7 0.1 The Lebesgue integral ------7 0.2 Some functional analysis ------18 0.3 Basic function spaces ------25 0.4 Comments on Chapter 0------43 0.5 Exercises to Chapter 0------46 1 Classical BV-spaces ------55 1.1 Functions of bounded variation ------55 1.2 Bounded variation and continuity ------71 1.3 Functions of bounded Wiener variation -----84 1.4 Functions of several variables ------91 1.5 Comments on Chapter 1------100 1.6 Exercises to Chapter 1------104 2 Nonclassical BV-spaces ------112 2.1 The Wiener-Young variation ------112 2.2 The Waterman variation ------125 2.3 The Schramm variation ------152 2.4 The Riesz-Medvedev variation ------161 2.5 The Korenblum variation ------169 2.6 Higher order Wiener-type variations ------182 2.7 Comments on Chapter 2------187 2.8 Exercises to Chapter 2------202 3 Absolutely continuous functions ------208 3.1 Continuity and absolute continuity ------208 3.2 The Vitali-Banach-Zaretskij theorem ------211 3.3 Reconstructing a function from its derivative ------218 3.4 Rectifiable functions ------231 3.5 The Riesz-Medvedev theorem ------240 3.6 Higher order Riesz-type variations ------244 3.7 Comments on Chapter 3------249 3.8 Exercises to Chapter 3------260 Χ —- Contents 4 Riemann-Stieltfes integrals ------268 4.1 Classical RS-integrals ------268 4.2 Bounded variation and duality ------292 4.3 Bounded p-variation and duality ------298 4.4 Nonclassical RS-integrals ------302 4.5 Comments on Chapter 4------311 4.6 Exercises to Chapter 4------316 5 Nonlinear composition operators ------324 5.1 The composition operator problem ------324 5.2 Boundedness and continuity ------344 5.3 Spaces of differentiable functions ------354 5.4 Global Lipschitz continuity ------364 5.5 Local Lipschitz continuity ------368 5.6 Comments on Chapter 5------377 5.7 Exercises to Chapter 5------382 6 Nonlinear superposition operators ------385 6Λ Boundedness and continuity ------385 6.2 Lipschitz continuity ------400 6.3 Uniform boundedness and continuity ------406 6.4 Functions of several variables ------415 6.5 Comments on Chapter 6-----419 6.6 Exercises to Chapter 6-----423 7 Some applications -----425 7.1 Convergence criteria for Fourier series ------425 7.2 Fourier series and Waterman spaces ------429 7.3 Applications to nonlinear integral equations ------435 7.4 Comments on Chapter 7------444 References ------453 List of functions ------467 List of symbols ------468 Index ------472 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. The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.
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indexdate	2024-12-20T16:12:00Z
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isbn	9783110265071 9783110266245
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-025157099
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physical	X, 476 S. graph. Darst.
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publisher	De Gruyter
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series	de Gruyter series in nonlinear analysis and applications
series2	de Gruyter series in nonlinear analysis and applications
spellingShingle	Appell, Jürgen 1952- Banaś, Józef Merentes Díaz, Nelson José 1954- Bounded variation and around de Gruyter series in nonlinear analysis and applications Harmonische Analyse (DE-588)4023453-8 gnd Funktion von beschränkter Variation (DE-588)4155666-5 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd
subject_GND	(DE-588)4023453-8 (DE-588)4155666-5 (DE-588)4177490-5
title	Bounded variation and around
title_auth	Bounded variation and around
title_exact_search	Bounded variation and around
title_full	Bounded variation and around Jürgen Appell ; Józef Banas ; Nelson Merentes
title_fullStr	Bounded variation and around Jürgen Appell ; Józef Banas ; Nelson Merentes
title_full_unstemmed	Bounded variation and around Jürgen Appell ; Józef Banas ; Nelson Merentes
title_short	Bounded variation and around
title_sort	bounded variation and around
topic	Harmonische Analyse (DE-588)4023453-8 gnd Funktion von beschränkter Variation (DE-588)4155666-5 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd
topic_facet	Harmonische Analyse Funktion von beschränkter Variation Nichtlineare Analysis
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025157099&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025157099&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV005530011
work_keys_str_mv	AT appelljurgen boundedvariationandaround AT banasjozef boundedvariationandaround AT merentesdiaznelsonjose boundedvariationandaround

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