Publication 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

journal article - other

Language

en

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

RIV year

2010

Released

01.10.2010

Pages from

439

Pages to

448

Pages count

10

BibTex

``````
@article{BUT50468,
author="Jiří {Vítovec} and Pavel {Řehák}",
title="Regular variation on measure chains",
annote="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.",
chapter="50468",
journal="Nonlinear Analysis, Theory, Methods and Applications",
number="1",
volume="72",
year="2010",
month="october",
pages="439--448",
type="journal article - other"
}``````