Detail publikačního výsledku

Regular variation on measure chains

VÍTOVEC, J.; ŘEHÁK, P.

Originální název

Regular variation on measure chains

Anglický název

Regular variation on measure chains

Druh

Článek recenzovaný mimo WoS a Scopus

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

VÍTOVEC, J.; ŘEHÁK, P.

Rok RIV

2011

Vydáno

01.10.2010

ISSN

0362-546X

Periodikum

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Svazek

72

Číslo

1

Stát

Spojené království Velké Británie a Severního Irska

Strany od

439

Strany do

448

Strany počet

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"
}