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2016 | OriginalPaper | Chapter

On Summability, Multipliability, and Integrability

Authors : Seppo Heikkilä, Antonín Slavík

Published in: Current Topics in Summability Theory and Applications

Publisher: Springer Singapore

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Abstract

We define and study summability and multipliability of families indexed by well-ordered sets of real numbers. These concepts generalize the classical notions of convergence of infinite series and products. The members of the families are assumed to be elements of general Banach spaces or Banach algebras, but most of our results are new even in the real-valued case. Our studies are also motivated by problems in integration theory of functions of one variable. In particular, we describe the relation between integrability and product integrability on one side, and summability and multipliability on the other side. Applications in the theory of differential equations with impulses and distributional differential equations are presented, and concrete examples are introduced to illustrate the derived theoretical results.

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previous chapter Convergence Acceleration and Improvement by Regular Matrices

next chapter Multi-dimensional Summability Theory and Continuous Wavelet Transform

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Title: On Summability, Multipliability, and Integrability
Authors: Seppo Heikkilä
Antonín Slavík
Publisher: Springer Singapore
Book: Current Topics in Summability Theory and Applications
Print ISBN: 978-981-10-0912-9

Electronic ISBN: 978-981-10-0913-6

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-981-10-0913-6_5

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