Publication detail

Refined discrete regular variation and its applications

ŘEHÁK, P.

Original Title

Refined discrete regular variation and its applications

English Title

Refined discrete regular variation and its applications

Type

journal article in Web of Science

Language

en

Original Abstract

We introduce a new class of the so-called regularly varying sequences with respect to tau and state its properties. This class, on one hand, generalizes regularly varying sequences. On the other hand, it refines them and makes it possible to do a more sophisticated analysis in applications. We show a close connection with regular variation on time scales; thanks to this relation, we can use the existing theory on time scales to develop discrete regular variation with respect to tau. We reveal also a connection with generalized regularly varying functions. As an application, we study asymptotic behavior of solutions to linear difference equations; we obtain generalization and extension of known results. The theory also yields, in some way, a new view on the tests for convergence and divergence of series; we establish the statement that generalizes Raabe test and Bertrand test.

English abstract

We introduce a new class of the so-called regularly varying sequences with respect to tau and state its properties. This class, on one hand, generalizes regularly varying sequences. On the other hand, it refines them and makes it possible to do a more sophisticated analysis in applications. We show a close connection with regular variation on time scales; thanks to this relation, we can use the existing theory on time scales to develop discrete regular variation with respect to tau. We reveal also a connection with generalized regularly varying functions. As an application, we study asymptotic behavior of solutions to linear difference equations; we obtain generalization and extension of known results. The theory also yields, in some way, a new view on the tests for convergence and divergence of series; we establish the statement that generalizes Raabe test and Bertrand test.

Keywords

Regularly varying sequence; Karamata theorem; time scale; difference equation; asymptotic behavior; Raabe test; Bertrand test

Released

23.07.2019

Publisher

John Wiley & Sons Ltd

Location

Velká Británie

Pages from

1

Pages to

12

Pages count

12

URL

Documents

BibTex


@article{BUT157903,
  author="Pavel {Řehák}",
  title="Refined discrete regular variation and its applications",
  annote="We introduce a new class of the so-called regularly varying sequences with respect to tau and state its properties. This class, on one hand, generalizes regularly varying sequences. On the other hand, it refines them and makes it possible to do a more sophisticated analysis in applications. We show a close connection with regular variation on time scales; thanks to this relation, we can use the existing theory on time scales to develop discrete regular variation with respect to tau. We reveal also a connection with generalized regularly varying functions. As an application, we study asymptotic behavior of solutions to linear difference equations; we obtain generalization and extension of known results. The theory also yields, in some way, a new view on the tests for convergence and divergence of series; we establish the statement that generalizes Raabe test and Bertrand test.",
  address="John Wiley & Sons Ltd",
  chapter="157903",
  doi="10.1002/mma.5670",
  howpublished="online",
  institution="John Wiley & Sons Ltd",
  number="18",
  volume="42",
  year="2019",
  month="july",
  pages="1--12",
  publisher="John Wiley & Sons Ltd",
  type="journal article in Web of Science"
}