Abstract

We show that $$ is a Gabor frame when $a>0, b>0, ab 0$. This is accomplished by expressing the Zak transform of $g_2$ in terms of the Zak transform of the Gaussian $g_1=^{{1/4}} \exp $, together with an appropriate use of the Ron-Shen criterion for being a Gabor frame. As a side result it follows that the windows, generating tight Gabor frames, that are canonically associated to $g_2$ and $g_1$ are the same at critical density $a=b=1$. Also, we display the ``singular'' dual function corresponding to the hyperbolic secant at critical density.