Regular variation on measure chains

J 2010

Regular variation on measure chains

ŘEHÁK, Pavel and Jiří VÍTOVEC

Basic information

Original name

Regular variation on measure chains

Name in Czech

Regulární variace na měřitelných řetězcích

Authors

ŘEHÁK, Pavel (203 Czech Republic, guarantor) and Jiří VÍTOVEC (203 Czech Republic, belonging to the institution)

Edition

Nonlinear Analysis, Theory, Methods & Applications, Elsevier Science Ltd. 2010, 0362-546X

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.279

RIV identification code

RIV/00216224:14310/10:00049385

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1016/j.na.2009.06.078

UT WoS

000272573900041

Keywords (in Czech)

regulárně se měnící funkce; time scales; věta o vnoření; věta o reprezentaci; lineární dynamická rovnice

Keywords in English

Regularly varying function; Regularly varying sequence; Measure chain; Time scale; Embedding theorem; Representation theorem; Second order dynamic equation; Asymptotic properties

Abstract

ORIG CZ

V originále

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.

In Czech

Ukazujeme souvislosti mezi nedávno zavedenou definicí regulární variace pomocí delta derivace a definicí Karamatova typu. Je dokázána věta o vnoření a reprezentaci. Je ukázáno, že pro rozumnou teorii je potřeba dodatečného předpokladu na zrnitost. Jsou odvozeny různé vlastnosti regulárně se měnících funkcí. Teorie je aplikována při popisu asymptotických vlastností řešení dynamických rovnic druhého řádu.

Links

GA201/07/0145, research and development project

Name: Diferenční rovnice a dynamické rovnice na ,,time scales'' II

Investor: Czech Science Foundation, Difference equations and dynamic equations on time scales II

Citovat

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.

@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.

Detailed Information on Publication Record