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VÍTOVEC, J. ŘEHÁK, P.
Originální název
Regular variation on measure chains
Typ
článek v časopise - ostatní, Jost
Jazyk
angličtina
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.
Klíčová slova
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
2010
Vydáno
1. 10. 2010
ISSN
0362-546X
Periodikum
Nonlinear Analysis, Theory, Methods and Applications
Ročník
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 and Applications", year="2010", volume="72", number="1", pages="439--448", issn="0362-546X" }