Regular variation on measure chains |
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Authors: | Pavel ?ehák Ji?í Vítovec |
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Institution: | a Institute of Mathematics, Academy of Sciences of the Czech Republic, ?i?kova 22, 61662 Brno, Czech Republic b Department of Mathematical Analysis, Faculty of Science, Masaryk University Brno, Kotlá?ská 2, 61137 Brno, Czech Republic |
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Abstract: | 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. |
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Keywords: | 26A12 26A99 34C11 39A11 39A12 |
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