Publication result detail

Regular variation on measure chains

VÍTOVEC, J.; ŘEHÁK, P.

Original Title

Regular variation on measure chains

English Title

Regular variation on measure chains

Type

Peer-reviewed article not indexed in WoS or Scopus

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.

English 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

Key words in English

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

2011

Released

01.10.2010

ISBN

0362-546X

Periodical

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Volume

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 & APPLICATIONS",
  year="2010",
  volume="72",
  number="1",
  pages="439--448",
  issn="0362-546X"
}