Metric Modular Spaces

1. Auflage 2015
ISBN: 978-3-319-25281-0
Verlag: Springer Nature Switzerland

Buch, Englisch, 137 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2409 g

Reihe: SpringerBriefs in Mathematics

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. 

Zielgruppe

Research

Autoren/Hrsg.

Chistyakov, Vyacheslav

Fachgebiete

• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

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.