ŘEHÁK, Pavel and Jiří VÍTOVEC. Regular variation on measure chains. Nonlinear Analysis, Theory, Methods & Applications. Elsevier Science Ltd., 2010, vol. 72, No 1, p. 439-448. ISSN 0362-546X. Available from: https://dx.doi.org/10.1016/j.na.2009.06.078. |
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@article{855462, author = {Řehák, Pavel and Vítovec, Jiří}, article_number = {1}, doi = {http://dx.doi.org/10.1016/j.na.2009.06.078}, keywords = {Regularly varying function; Regularly varying sequence; Measure chain; Time scale; Embedding theorem; Representation theorem; Second order dynamic equation; Asymptotic properties}, language = {eng}, issn = {0362-546X}, journal = {Nonlinear Analysis, Theory, Methods & Applications}, title = {Regular variation on measure chains}, url = {http://dx.doi.org/10.1016/j.na.2009.06.078}, volume = {72}, year = {2010} }
TY - JOUR ID - 855462 AU - Řehák, Pavel - Vítovec, Jiří PY - 2010 TI - Regular variation on measure chains JF - Nonlinear Analysis, Theory, Methods & Applications VL - 72 IS - 1 SP - 439-448 EP - 439-448 PB - Elsevier Science Ltd. SN - 0362546X KW - Regularly varying function KW - Regularly varying sequence KW - Measure chain KW - Time scale KW - Embedding theorem KW - Representation theorem KW - Second order dynamic equation KW - Asymptotic properties UR - http://dx.doi.org/10.1016/j.na.2009.06.078 L2 - http://dx.doi.org/10.1016/j.na.2009.06.078 N2 - 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. ER -
ŘEHÁK, Pavel and Jiří VÍTOVEC. Regular variation on measure chains. \textit{Nonlinear Analysis, Theory, Methods \&{} Applications}. Elsevier Science Ltd., 2010, vol.~72, No~1, p.~439-448. ISSN~0362-546X. Available from: https://dx.doi.org/10.1016/j.na.2009.06.078.
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