Metric modular spaces

by Chistyakov, Vyacheslav

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Title Statements

Full title :Metric modular spaces / Vyacheslav Chistyakov.

Summary

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℗ℓ 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.℗ℓ.

Edition Statements

Publication Date:2015.

Publication Statements

Publisher(s):Springer
Place of Publication:Cham
Language:eng
Publication Date:2015.

The Physical Object

Description:1 volume ; : 24 cm

Edition Identifiers

ISBN:9783319252810, 331925281X
oclc:on1062278041
LC Classification:QA331.7
Dewey Decimal:514.325

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.