Geodesic
On sums of binomial coefficients, wavelets, complex anallysis and operator theory
Ondrej Hutník1 ; Mária Hutníková2 ; Ondrej Hutník ; Mária Hutníková
1Institute of Mathematics, Faculty of Science, Pavol Jozef Šafárik University in Košice, Slovakia
2Department of Physics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Slovakia
Acta mathematica Universitatis Comenianae, Tome 89 (2020) no. 2, pp. 215-223 
Ondrej Hutník; Mária Hutníková; Ondrej Hutník; Mária Hutníková. On sums of binomial coefficients, wavelets, complex anallysis and operator theory. Acta mathematica Universitatis Comenianae, Tome 89 (2020) no. 2, pp. 215-223. http://geodesic.mathdoc.fr/item/AMUC_2020_89_2_a2/
@article{AMUC_2020_89_2_a2,
     author = {Ondrej Hutn{\'\i}k and M\'aria Hutn{\'\i}kov\'a and Ondrej Hutn{\'\i}k and M\'aria Hutn{\'\i}kov\'a},
     title = { On sums of binomial coefficients, wavelets, complex anallysis and operator theory},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {215--223},
     year = {2020},
     volume = {89},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2020_89_2_a2/}
}
TY  - JOUR
AU  - Ondrej Hutník
AU  - Mária Hutníková
AU  - Ondrej Hutník
AU  - Mária Hutníková
TI  - On sums of binomial coefficients, wavelets, complex anallysis and operator theory
JO  - Acta mathematica Universitatis Comenianae
PY  - 2020
SP  - 215
EP  - 223
VL  - 89
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AMUC_2020_89_2_a2/
ID  - AMUC_2020_89_2_a2
ER  - 
%0 Journal Article
%A Ondrej Hutník
%A Mária Hutníková
%A Ondrej Hutník
%A Mária Hutníková
%T On sums of binomial coefficients, wavelets, complex anallysis and operator theory
%J Acta mathematica Universitatis Comenianae
%D 2020
%P 215-223
%V 89
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_2020_89_2_a2/
%F AMUC_2020_89_2_a2

Voir la notice de l'article provenant de la source Comenius University

In this short note we describe and demonstrate an interesting (analytical) tool for evaluating certain (discrete) sums of binomial coefficients. Its essence consists in complex analysis observation that spectral functions of Toeplitz operators acting on the true-poly-analytic Bergman spaces over the upper half-plane with a vertical symbol can be written as a sum of spectral functions of Toeplitz operators acting on weighted Bergman spaces. This connection is expressed using Laguerre functions and demonstrated on a few examples to get a closed form of certain sums. Our note contibutes to a demonstration how "continuous" mathematics may serve as a useful tool for purposes of "discrete" mathematics.