This article is cited in 1 paper

Limit Properties of Systems of Integer Translates and Functions Generating Tight Gabor Frames

E. A. Kiselev, L. A. Minin, I. Ya. Novikov

Voronezh State University

Abstract: This paper deals with one-parameter families of integer translates of functions. It is shown that, as the scaling multiplier tends to infinity, the nodal interpolation functions converge to the sample function and the ratio of the upper and lower Riesz constants tends to $2$. The assertion about convergence in the limit to the sample function is also proved for functions obtained by orthogonalization of the system of translates of the Gauss function and for the tight Gabor window functions as the ratio of the parameters of the time-frequency window tends to infinity.

Keywords: translate of a function, scaling multiplier, Gabor frame.

UDC: 517.518.8+517.988.8

Received: 19.10.2017
Revised: 26.07.2018

DOI: 10.4213/mzm11832

 English version: Mathematical Notes, 2019, 106:1, 71–80

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