Detail publikace

# Regular variation on measure chains

VÍTOVEC, J. ŘEHÁK, P.

Originální název

Regular variation on measure chains

Anglický název

Regular variation on measure chains

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Dokumenty

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"
}``````