Detail publikace

Refined discrete regular variation and its applications

ŘEHÁK, P.

Anglický název

Refined discrete regular variation and its applications

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova anglicky

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

Vydáno

23.07.2019

Nakladatel

John Wiley & Sons Ltd

Místo

Velká Británie

ISSN

1099-1476

Ročník

42

Číslo

18

Strany od–do

1–12

Počet stran

12

BIBTEX


@article{BUT157903,
  author="Pavel {Řehák},
  title="Refined discrete regular variation and its applications",
  year="2019",
  volume="42",
  number="18",
  month="July",
  pages="1--12",
  publisher="John Wiley & Sons Ltd ",
  address="Velká Británie",
  issn="1099-1476"
}