Regular variation on measure chains

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Authors	ŘEHÁK Pavel VÍTOVEC Jiří
Year of publication	2010
Type	Article in Periodical
Magazine / Source	Nonlinear Analysis, Theory, Methods & Applications
MU Faculty or unit	Faculty of Science
Citation
Web	http://dx.doi.org/10.1016/j.na.2009.06.078
Doi	http://dx.doi.org/10.1016/j.na.2009.06.078
Field	General mathematics
Keywords	Regularly varying function; Regularly varying sequence; Measure chain; Time scale; Embedding theorem; Representation theorem; Second order dynamic equation; Asymptotic properties
Description	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.
Related projects:	Difference equations and dynamic equations on time scales II