Flexible time-frequency expansions

By now Gabor analysis is a mature subfield of time-frequency analysis. It is well understood that for any lattice $\Lambda$ in the TF-plane the corresponding Gabor family $(\pi(\lambda)g)$
is a Gabor frame with good properties if the Gabor atom $g$ is a nice function, because
the commutation properties of the frame operator $S$ imply that also the dual atom $\gd$ has good properties. Generalizations of Wiener's inversion theorem, the Wexler-Raz biorthogonality and the use of the Janssen representation are powerful tools, and the corresponding Gabor families are robust (against various kinds of perturbations) and allow the characterization of distributions in various types of modulation spaces.

The recent development of localization theory (as proposed by K.~Groechenig and followers) allows to have similar properties for systems which behave only locally like lattices, without any global algebraic restrictions on the set $\Lambda$, in other words
we will discuss properties of irregular, semi-reqular, warped and otherwise distorted or slowly changing Gabor-like families.