This article is cited in 14 papers

On the Riesz Constants for Systems of Integer Translates

E. A. Kiselev^a, L. A. Minin^a, I. Ya. Novikov^a, S. M. Sitnik<sup>b

a</sup> Voronezh State University
^b Voronezh Institute of Russian Ministry of Internal Affairs

Abstract: In this paper, one-parameter families of integer translates of the Gaussian and Lorentz functions are studied. For a Lorentz function, we obtain formulas for the coefficients of the series defining node functions and show that the limit value of node functions is given by a sample function. For systems of translates generated by the Gaussian and Lorentz functions as well as by the node functions related to them, we obtain explicit expressions for the Riesz constants and study the parameter-dependent behavior of these constants. While proving some of the results of this paper, we establish the monotonicity of a special ratio of two Jacobi theta functions, a fact which is of interest in itself.

Keywords: Riesz constant, Gaussian function, Lorentz function, system of integer translates, node function, Jacobi theta function, Riesz system.

UDC: 517.518.8+517.988.8

Received: 29.08.2013
Revised: 02.12.2013

DOI: 10.4213/mzm10386

 English version: Mathematical Notes, 2014, 96:2, 228–238

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