Other formats:
BibTeX
LaTeX
RIS
@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., vol.~72, No~1, p.~439-448. ISSN~0362-546X. doi:10.1016/j.na.2009.06.078. 2010.
|
