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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
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Volume 10, Issue 1

Issues

Local Growth of Weierstrass σ-Function and Whittaker-Type Derivative Sampling

Tibor K. Pogány
  • Faculty of Maritime Studies, University of Rijeka, 51000 Rijeka, Studentska 2, Croatia. E-mail:
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Published Online: 2010-02-26 | DOI: https://doi.org/10.1515/GMJ.2003.157

Abstract

Two explicit guard functions 𝐾𝑗= 𝐾𝑗(δ 𝑧), 𝑗 = 1, 2, are obtained, which depend on the distance δ 𝑧 between 𝑧 and the nearest point of the integer lattice in the complex plane, such that δ 𝑧𝐾1(δ 𝑧) ≤ |σ(𝑧)|𝑒–π|𝑧|2/2δ 𝑧𝐾2(δ 𝑧), 𝑧 ∈ ℂ, where σ(𝑧) stands for the Weierstraß σ-function. This result is used to improve the circular truncation error upper bound in the 𝑞-th order Whittaker-type derivative sampling for the Leont'ev functions space .

Key words and phrases:: Circular truncation error; derivative sampling; entire function spaces [ρ, 𝜓], [ρ, 𝜓); sampling truncation error upper bound; Weierstraß σ-function; Whittaker-type derivative sampling reconstruction

About the article

Received: 2001-07-02

Revised: 2002-09-21

Published Online: 2010-02-26

Published in Print: 2003-03-01


Citation Information: Georgian Mathematical Journal, Volume 10, Issue 1, Pages 157–164, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/GMJ.2003.157.

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[1]
Tibor K. Pogány
Applied Mathematics and Computation, 2007, Volume 187, Number 1, Page 384

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