Regular variation on measure chains
| Authors | |
|---|---|
| Year of publication | 2010 |
| Type | Article in Periodical |
| Magazine / Source | Nonlinear Analysis, Theory, Methods & Applications |
| MU Faculty or unit | |
| 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. |
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