Gabor frame operator for the Cauchy kernel

Abstract

We obtain frame bounds estimates and the Gabor frame operator $S=S^{\alpha ,\beta }$ for Gabor frames generated by the Cauchy kernel. In addition we find the explicit expression for the canonical dual window for all values of the lattice parameters $\alpha ,\beta$, $\alpha \beta \le 1$.

Submitted August 15, 2022 to Ufa Mathematical Journal