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Regular variation on measure chains

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    0333009 - MÚ 2010 RIV GB eng J - Journal Article
    Řehák, Pavel - Vitovec, J.
    Regular variation on measure chains.
    [Regulární variace na měřitelných žetězcích.]
    Nonlinear Analysis: Theory, Methods & Applications. Roč. 72, č. 1 (2010), s. 439-448. ISSN 0362-546X. E-ISSN 1873-5215
    R&D Projects: GA AV ČR KJB100190701
    Institutional research plan: CEZ:AV0Z10190503
    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
    Impact factor: 1.279, year: 2010
    http://www.sciencedirect.com/science/article/pii/S0362546X09008475

    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.

    Ukazujeme souvislosti mezi nedávno zavedenou definicí regulární variace pomocí delta derivace a definicí Karamatova typu. Je dokázána věta o vnoření a reprezentaci. Je ukázáno, že pro rozumnou teorii je potřeba dodatečného předpokladu na zrnitost. Jsou odvozeny různé vlastnosti regulárně se měnících funkcí. teorie je aplikována při popisu asymptotických vlastností řazení dynamických rovnic druhého řádu.
    Permanent Link: http://hdl.handle.net/11104/0178101

     
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