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Zustand: New. 1st ed. 2021 edition NO-PA16APR2015-KAP.
Sprache: Englisch
Verlag: Springer International Publishing, 2021
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The book addresses the minimization of special lower semicontinuous functionals over closed balls in metric spaces, called the approximate variation. The new notion of approximate variation contains more information about the bounded variation functi…onal and has the following features: the infimum in the definition of approximate variation is not attained in general and the total Jordan variation of a function is obtained by a limiting procedure as a parameter tends to zero. By means of the approximate variation, we are able to characterize regulated functions in a generalized sense and provide powerful compactness tools in the topology of pointwise convergence, conventionally called pointwise selection principles.The book presents a thorough, self-contained study of the approximate variation and results which were not published previously in book form. The approximate variation is illustrated by a large number of examples designed specifically for this study. The discussion elaborates on the state-of-the-art pointwise selection principles applied to functions with values in metric spaces, normed spaces, reflexive Banach spaces, and Hilbert spaces. The highlighted feature includes a deep study of special type of lower semicontinuous functionals though the applied methods are of a general nature. The content is accessible to students with some background in real analysis, general topology, and measure theory.Among the new results presented are properties of the approximate variation: semi-additivity, change of variable formula, subtle behavior with respect to uniformly and pointwise convergent sequences of functions, and the behavior on improper metric spaces. These properties are crucial for pointwise selection principles in which the key role is played by the limit superior of the approximate variation. Interestingly, pointwise selection principles may be regular, treating regulated limitfunctions, and irregular, treating highly irregular functions (e.g., Dirichlet-type functions), in which a significant role is played by Ramsey's Theorem from formal logic.
Weitere BilderSprache: Englisch
Verlag: Springer, 2021
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Taschenbuch. Zustand: Neu. From Approximate Variation to Pointwise Selection Principles | Vyacheslav V. Chistyakov | Taschenbuch | SpringerBriefs in Optimization | xiii | Englisch | 2021 | Springer | EAN 9783030873981 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hart…mann[at]springer[dot]com | Anbieter: preigu.
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The book addresses the minimization of special lower semicontinuous functionals over closed balls in metric spaces, called the approximate variation. The new notion of approximate variation contains more information about the bounded…variation functional and has the following features: the infimum in the definition of approximate variation is not attained in general and the total Jordan variation of a function is obtained by a limiting procedure as a parameter tends to zero. By means of the approximate variation, we are able to characterize regulated functions in a generalized sense and provide powerful compactness tools in the topology of pointwise convergence, conventionally called pointwise selection principles.The book presents a thorough, self-contained study of the approximate variation and results which were not published previously in book form. The approximate variation is illustrated by a large number of examples designed specifically for this study. The discussion elaborates on the state-of-the-art pointwise selection principles applied to functions with values in metric spaces, normed spaces, reflexive Banach spaces, and Hilbert spaces. The highlighted feature includes a deep study of special type of lower semicontinuous functionals though the applied methods are of a general nature. The content is accessible to students with some background in real analysis, general topology, and measure theory.Among the new results presented are properties of the approximate variation: semi-additivity, change of variable formula, subtle behavior with respect to uniformly and pointwise convergent sequences of functions, and the behavior on improper metric spaces. These properties are crucial for pointwise selection principles in which the key role is played by the limit superior of the approximate variation. Interestingly, pointwise selection principles may be regular, treating regulated limitfunctions, and irregular, treating highly irregular functions (e.g., Dirichlet-type functions), in which a significant role is played by Ramsey's Theorem from formal logic. 100 pp. Englisch.
Sprache: Englisch
Verlag: Springer, 2021
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Kartoniert / Broschiert. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Explicit evaluation and approximation of bounded variation functionals on metric spacesHighlighted feature includes a deep study of a special type of lower semicontinuous functionalsAccessible t…o upper undergraduate students taking courses .
Sprache: Englisch
Verlag: Springer, Palgrave Macmillan Okt 2021, 2021
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Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -The book addresses the minimization of special lower semicontinuous functionals over closed balls in metric spaces, called the approximate variation. The new notion of approximate variation contains more information about the bounded vari…ation functional and has the following features: the infimum in the definition of approximate variation is not attained in general and the total Jordan variation of a function is obtained by a limiting procedure as a parameter tends to zero. By means of the approximate variation, we are able to characterize regulated functions in a generalized sense and provide powerful compactness tools in the topology of pointwise convergence, conventionally called pointwise selection principles.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 100 pp. Englisch.
