Publication detail

Regular variation on measure chains

VÍTOVEC, J. ŘEHÁK, P.

Original Title

Regular variation on measure chains

Type

journal article - other

Language

English

Original 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

Authors

VÍTOVEC, J.; ŘEHÁK, P.

RIV year

2010

Released

1. 10. 2010

ISBN

0362-546X

Periodical

Nonlinear Analysis, Theory, Methods and Applications

Year of study

72

Number

1

State

United Kingdom of Great Britain and Northern Ireland

Pages from

439

Pages to

448

Pages count

10

BibTex

@article{BUT50468,
  author="Jiří {Vítovec} and Pavel {Řehák}",
  title="Regular variation on measure chains",
  journal="Nonlinear Analysis, Theory, Methods and Applications",
  year="2010",
  volume="72",
  number="1",
  pages="439--448",
  issn="0362-546X"
}