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Mathematical Notes

, Volume 96, Issue 1–2, pp 228–238 | Cite as

On the Riesz constants for systems of integer translates

  • E. A. Kiselev
  • L. A. Minin
  • I. Ya. Novikov
  • S. M. Sitnik
Article

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 

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • E. A. Kiselev
    • 1
  • L. A. Minin
    • 1
  • I. Ya. Novikov
    • 1
  • S. M. Sitnik
    • 2
  1. 1.Voronezh State UniversityVoronezhRussia
  2. 2.Voronezh Institute of the Ministry of Internal Affairs of RussiaVoronezhRussia

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