Result Details

Regular variation on measure chains

VÍTOVEC, J.; ŘEHÁK, P. Regular variation on measure chains. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, vol. 72, no. 1, p. 439-448. ISSN: 0362-546X.
Type
journal article
Language
English
Authors
Vítovec Jiří, Mgr., Ph.D., UMAT (FEEC)
Řehák Pavel, prof. Mgr., Ph.D.
Abstract

In this paper we show how the recently introduced concept of regular variation on time scales (or measure chains) is related to a Karamata type definition. We also present characterization theorems and an embedding theorem for regularly varying functions defined on suitable subsets of reals. We demonstrate that for a reasonable theory of regular variation on time scales, certain additional condition on a graininess is needed, which cannot be omitted. We establish a number of elementary properties of regularly varying functions. As an application, we study the asymptotic properties of solution to second order dynamic equations.

Keywords

Regularly varying function; Regularly varying sequence; Measure chain; Time scale; Embedding theorem; Representation theorem; Second order dynamic equation; Asymptotic properties

Published
2010
Pages
439–448
Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol. 72, no. 1, ISSN 0362-546X
BibTeX 
@article{BUT50468,
  author="Jiří {Vítovec} and Pavel {Řehák}",
  title="Regular variation on measure chains",
  journal="NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS",
  year="2010",
  volume="72",
  number="1",
  pages="439--448",
  issn="0362-546X"
}
Departments
Department of Mathematics (UMAT)
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