Publication detail

Lerch's theorem on nabla time scales

KISELA, T. DOLNÍK, M.

Original Title

Lerch's theorem on nabla time scales

English Title

Lerch's theorem on nabla time scales

Type

journal article in Web of Science

Language

en

Original Abstract

The paper discusses uniqueness of Laplace transform considered on nabla time scales. As the main result, a nabla time scales analogue of Lerch's theorem ensuring uniqueness of Laplace image is proved for so-called simply periodic time scales. Moreover, several presented counterexamples demonstrate that the uniqueness of Laplace image does not occur on general time scales when the nabla approach is employed. Other special properties of Laplace transform on nabla time scales, such as potential disconnectedness of domain of convergence, are addressed as well.

English abstract

The paper discusses uniqueness of Laplace transform considered on nabla time scales. As the main result, a nabla time scales analogue of Lerch's theorem ensuring uniqueness of Laplace image is proved for so-called simply periodic time scales. Moreover, several presented counterexamples demonstrate that the uniqueness of Laplace image does not occur on general time scales when the nabla approach is employed. Other special properties of Laplace transform on nabla time scales, such as potential disconnectedness of domain of convergence, are addressed as well.

Keywords

Lerch's theorem; Laplace transform; time scales theory; uniqueness; fractional calculus

Released

25.10.2019

Publisher

Walter de Gruyter GmbH

Location

GENTHINER STRASSE 13, D-10785 BERLIN, GERMANY

Pages from

1127

Pages to

1136

Pages count

10

URL

Documents

BibTex


@article{BUT159356,
  author="Tomáš {Kisela} and Matej {Dolník}",
  title="Lerch's theorem on nabla time scales",
  annote="The paper discusses uniqueness of Laplace transform considered on nabla time scales. As the main result, a nabla time scales analogue of Lerch's theorem ensuring uniqueness of Laplace image is proved for so-called simply periodic time scales. Moreover, several presented counterexamples demonstrate that the uniqueness of Laplace image does not occur on general time scales when the nabla approach is employed. Other special properties of Laplace transform on nabla time scales, such as potential disconnectedness of domain of convergence, are addressed as well.",
  address="Walter de Gruyter GmbH",
  chapter="159356",
  doi="10.1515/ms-2017-0295",
  howpublished="print",
  institution="Walter de Gruyter GmbH",
  number="5",
  volume="69",
  year="2019",
  month="october",
  pages="1127--1136",
  publisher="Walter de Gruyter GmbH",
  type="journal article in Web of Science"
}