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Regular variation on measure chains
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SYSNO ASEP 0333009 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Regular variation on measure chains Title Regulární variace na měřitelných žetězcích Author(s) Řehák, Pavel (MU-W) RID, SAI, ORCID
Vitovec, J. (CZ)Source Title Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier - ISSN 0362-546X
Roč. 72, č. 1 (2010), s. 439-448Number of pages 10 s. Language eng - English Country GB - United Kingdom Keywords regularly varying function ; regularly varying sequence ; measure chain ; time scale ; embedding theorem ; representation theorem ; second order dynamic equation ; asymptotic properties Subject RIV BA - General Mathematics R&D Projects KJB100190701 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000272573900041 EID SCOPUS 71749114346 DOI 10.1016/j.na.2009.06.078 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2010
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