Geodesic
Limit Properties of Systems of Integer Translates and Functions Generating Tight Gabor Frames
Matematičeskie zametki, Tome 106 (2019) no. 1, pp. 62-73

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2019_106_1_a5,
     author = {E. A. Kiselev and L. A. Minin and I. Ya. Novikov},
     title = {Limit {Properties} of {Systems} of {Integer} {Translates} and {Functions} {Generating} {Tight} {Gabor} {Frames}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {62--73},
     publisher = {mathdoc},
     volume = {106},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_1_a5/}
}
TY  - JOUR
AU  - E. A. Kiselev
AU  - L. A. Minin
AU  - I. Ya. Novikov
TI  - Limit Properties of Systems of Integer Translates and Functions Generating Tight Gabor Frames
JO  - Matematičeskie zametki
PY  - 2019
SP  - 62
EP  - 73
VL  - 106
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_106_1_a5/
LA  - ru
ID  - MZM_2019_106_1_a5
ER  - 
%0 Journal Article
%A E. A. Kiselev
%A L. A. Minin
%A I. Ya. Novikov
%T Limit Properties of Systems of Integer Translates and Functions Generating Tight Gabor Frames
%J Matematičeskie zametki
%D 2019
%P 62-73
%V 106
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_106_1_a5/
%G ru
%F MZM_2019_106_1_a5
E. A. Kiselev; L. A. Minin; I. Ya. Novikov. Limit Properties of Systems of Integer Translates and Functions Generating Tight Gabor Frames. Matematičeskie zametki, Tome 106 (2019) no. 1, pp. 62-73. http://geodesic.mathdoc.fr/item/MZM_2019_106_1_a5/