Linear independence of time-frequency shifts under a generalized Schrödinger representation

Kutyniok, Gitta (2002): Linear independence of time-frequency shifts under a generalized Schrödinger representation. In: Archiv der Mathematik, Vol. 78: pp. 135-144

Abstract

Let ρR​ be the classical Schrödinger representation of the Heisenberg group and let Λ be a finite subset of R×R. The question of when the set of functions {t↦e2πiytf(t+x)=(ρR(x,y,1)f)(t):(x,y)∈Λ}

is linearly independent for all f∈L2(R),f≠0, arises from Gabor analysis. We investigate an analogous problem for locally compact abelian groups G. For a finite subset Λ of G×G^

and ρG the Schrödinger representation of the Heisenberg group associated with G, we give a necessary and in many situations also sufficient condition for the set {ρG(x,w,1)f:(x,w)∈Λ}

to be linearly independent for all f∈L2(G),f≠0.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0003-889X
• Language: English