Naslov
A note on ell ^2-linear independence of Gabor systems

Autori
Slamić, Ivana

Vrsta, podvrsta
Radovi u časopisima, znanstveni

Izvornik
Collectanea Mathematica (2022)

Status rada
Online first

Ključne riječi
Integer translates ; Gabor system ; Unitary representation ; ℓ2-Linear independence ; Riesz projection

Sažetak
It is known that the system of integer translates of ψ∈L^2(R)∖{;0}; is ℓ^2(Z)-linearly independent precisely when the corresponding periodization function is strictly positive almost everywhere. The only known proof of this result is based on certain properties of the space of functions with uniformly bounded Fourier partial sums. We show that one of these properties does not hold for the analogue of this space in higher dimensions and square summation and, therefore, this method cannot be applied to solve the problem for integer translates of function ψ∈L^2(R^d) for d⩾2 or ℓ^2(Z^2d)-linear independence of Gabor systems {;T_kM_ℓψ:k, ℓ∈Zd}; for ψ∈L^2(R^d), with d⩾1.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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