Korean J. Math.  Vol 28, No 4 (2020)  pp.877-888
DOI: https://doi.org/10.11568/kjm.2020.28.4.877

Gabor frames in $l^2 (\mathbb Z)$ from Gabor frames in $L^2 (\mathbb R)$

Jineesh Thomas, Madhavan Namboothiri N M, Eldo Varghese

Abstract


In this paper we discuss about the image of Gabor frame under a unitary operator and derive a sufficient condition under which a unitary operator from $L^2 (\mathbb R)$ to $l^2 (\mathbb Z)$ maps Gabor frame in $L^2 (\mathbb R)$ to a Gabor frame in $l^2 (\mathbb Z)$.

Keywords


Hilbert space, Gabor frame, Orthonormal basis, Unitary operator, Window sequence.

Subject classification

42C15, 47B90, 94A12

Sponsor(s)



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