ABSTRACT

### Perturbation of Frames and Applications to {G}abor Frames

#### O. Christensen

##### email: olechr@mat.dtu.dk

We prove a stability result for frames, with a perturbation condition that generalizes the Paley-Wiener condition used in the context of bases. We show how the result can be applied to different types of perturbations of a Gabor frame $\{e^{imbx} f(x-na) \}_{m,n \in Z}$ of $L^2(R)$, e.g., perturbation of $f$ or $na$.