Metric modular spaces [electronic resource]

• 作者： Chistyakov, Vyacheslav V.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • SpringerBriefs in mathematics,
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： SpringerBriefs in mathematics,
• 主題： Metric spaces , Mathematics , Several Complex Variables and Analytic Spaces. , Ordinary Differential Equations. , Functional analysis , Special Functions.
• ISBN： 9783319252834 (electronic bk.) 、 9783319252810 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 1.Classes of Modulars -- 2. Metrics on Modular Spaces -- 3. Modular Transforms -- 4. Topologies on Modular Spaces -- 5. Bounded and Regulated Mappings -- 6. Mappings of Bounded Generalized Variation -- Appendix -- References.
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• 摘要註: Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity fields and serve two important purposes: generate metric spaces in a unified manner and provide a weaker convergence, the modular convergence, whose topology is non-metrizable in general. Metric modular spaces are extensions of metric spaces, metric linear spaces, and classical modular linear spaces. The topics covered include the classification of modulars, metrizability of modular spaces, modular transforms and duality between modular spaces, metric and modular topologies. Applications illustrated in this book include: the description of superposition operators acting in modular spaces, the existence of regular selections of set-valued mappings, new interpretations of spaces of Lipschitzian and absolutely continuous mappings, the existence of solutions to ordinary differential equations in Banach spaces with rapidly varying right-hand sides.
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