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 limit functions, 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.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Vyacheslav V. Chistyakov is Professor of Mathematics at the National Research University Higher School of Economics in Nizhny Novgorod, Russia. He received a PhD in Mathematics in 1987 from the Moscow State (Lomonosov) University, Moscow, Russia, and a D.Sc. in Mathematics in 2002 from the Sobolev Institute of Mathematics (Siberian Branch of Russian Academy of Sciences), Novosibirsk, Russia. His areas of research are real and functional analysis, set-valued analysis, optimization, and the decision making theory. He authored more than 100 research articles and several books including Metric Modular Spaces: Theory and Applications, Springer, 2015.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
EUR 4,69 expédition depuis Royaume-Uni vers France
Destinations, frais et délaisVendeur : Ria Christie Collections, Uxbridge, Royaume-Uni
Etat : New. In. N° de réf. du vendeur ria9783030873981_new
Quantité disponible : Plus de 20 disponibles
Vendeur : Chiron Media, Wallingford, Royaume-Uni
PF. Etat : New. N° de réf. du vendeur 6666-IUK-9783030873981
Quantité disponible : 10 disponible(s)
Vendeur : moluna, Greven, Allemagne
Kartoniert / Broschiert. Etat : 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 to upper undergraduate students taking courses . N° de réf. du vendeur 495743223
Quantité disponible : Plus de 20 disponibles
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
Taschenbuch. Etat : 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 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. N° de réf. du vendeur 9783030873981
Quantité disponible : 1 disponible(s)
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
Taschenbuch. Etat : 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. N° de réf. du vendeur 9783030873981
Quantité disponible : 2 disponible(s)
Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne
Taschenbuch. Etat : Neu. 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 100 pp. Englisch. N° de réf. du vendeur 9783030873981
Quantité disponible : 2 disponible(s)
Vendeur : California Books, Miami, FL, Etats-Unis
Etat : New. N° de réf. du vendeur I-9783030873981
Quantité disponible : Plus de 20 disponibles
Vendeur : Books Puddle, New York, NY, Etats-Unis
Etat : New. 1st ed. 2021 edition NO-PA16APR2015-KAP. N° de réf. du vendeur 26390224852
Quantité disponible : 4 disponible(s)
Vendeur : Majestic Books, Hounslow, Royaume-Uni
Etat : New. Print on Demand. N° de réf. du vendeur 389407755
Quantité disponible : 4 disponible(s)
Vendeur : Biblios, Frankfurt am main, HESSE, Allemagne
Etat : New. PRINT ON DEMAND. N° de réf. du vendeur 18390224862
Quantité disponible : 4 disponible(s)