info:eu-repo/semantics/article
Tiling functions and Gabor orthonormal basis
Fecha
2020-01Registro en:
Agora, Elona; Antezana, Jorge Abel; Kolountzakis, Mihail N.; Tiling functions and Gabor orthonormal basis; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 48; 1; 1-2020; 96-122
1063-5203
CONICET Digital
CONICET
Autor
Agora, Elona
Antezana, Jorge Abel
Kolountzakis, Mihail N.
Resumen
We study the existence of Gabor orthonormal bases with window the characteristic function of the set Ω=[0,α]∪[β+α,β+1] of measure 1, with α,β>0. By the symmetries of the problem, we can restrict our attention to the case α≤1/2. We prove that either if α<1/2 or (α=1/2 and β≥1/2) there exist such Gabor orthonormal bases, with window the characteristic function of the set Ω, if and only if Ω tiles the line. Furthermore, in both cases, we completely describe the structure of the set of time-frequency shifts associated to these bases.