  We study Gabor frames in the case when the window function is of hyperbolic
secant type, i.e., $g(x) = (e^x+ae^{-bx})^{-1}$, $a>0$, ${\rm Re}\, b>0$. A
criterion for half-irregular sampling is obtained: for a separated
$\Lambda\subset\mathbb{R}$ the Gabor system $\mathcal{G}(g, \Lambda \times
\alpha\mathbb{Z})$ is a frame in $L^2(\mathbb{R})$ if and only if $D^-(\Lambda)
>\alpha$ where $D^-(\Lambda)$ is the usual (Beurling) lower density of
$\Lambda$. Also, a full description of complete interpolating sequences for the
shift-invariant space generated by $g$ is given.

Functional Analysis;Complex Variables