Geodesic
Identifying continuous Gabor frames on locally compact Abelian groups
Filomat, Tome 37 (2023) no. 18, p. 6011

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

In this paper, we establish some necessary and sufficient conditions for constructing continuous Gabor frames in L 2 (G), where G is a second countable locally compact abelian (LCA) group. More precisely, we reformulate the generalized Zak transform defined by A. Weil on LCA groups and later proposed by GröchenigGr¨Gröchenig in the case of integer-oversampled lattices, however our approach is regarding the assumption that both translation and modulation groups are closed subgroups. Moreover, we discuss the possibility of such a generalization and apply several examples to demonstrate the necessity of standing conditions in the results. Finally, by using the generalized Zak transform and fiberization technique, we characterize the continuous Gabor frames of L 2 (G) in terms of a family of frames in l 2 (H ⊥) for a closed co-compact subgroup H of G.
DOI : 10.2298/FIL2318011H
Classification : 43A15, 42C15, 43A55, 41A25
Keywords: LCA group, Zak transform, Continuous Gabor frame, Fiberization technique 
Zohre Hamidi; Fahimeh Arabyani-Neyshaburi; Rajab A Kamyabi-Gol; Mohammad H Sattari. Identifying continuous Gabor frames on locally compact Abelian groups. Filomat, Tome 37 (2023) no. 18, p. 6011 . doi: 10.2298/FIL2318011H
@article{10_2298_FIL2318011H,
     author = {Zohre Hamidi and Fahimeh Arabyani-Neyshaburi and Rajab A Kamyabi-Gol and Mohammad H Sattari},
     title = {Identifying continuous {Gabor} frames on locally compact {Abelian} groups},
     journal = {Filomat},
     pages = {6011 },
     year = {2023},
     volume = {37},
     number = {18},
     doi = {10.2298/FIL2318011H},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2318011H/}
}
TY  - JOUR
AU  - Zohre Hamidi
AU  - Fahimeh Arabyani-Neyshaburi
AU  - Rajab A Kamyabi-Gol
AU  - Mohammad H Sattari
TI  - Identifying continuous Gabor frames on locally compact Abelian groups
JO  - Filomat
PY  - 2023
SP  - 6011 
VL  - 37
IS  - 18
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2318011H/
DO  - 10.2298/FIL2318011H
LA  - en
ID  - 10_2298_FIL2318011H
ER  - 
%0 Journal Article
%A Zohre Hamidi
%A Fahimeh Arabyani-Neyshaburi
%A Rajab A Kamyabi-Gol
%A Mohammad H Sattari
%T Identifying continuous Gabor frames on locally compact Abelian groups
%J Filomat
%D 2023
%P 6011 
%V 37
%N 18
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2318011H/
%R 10.2298/FIL2318011H
%G en
%F 10_2298_FIL2318011H

Cité par Sources :