Hilbert space valued Gabor frames in weighted amalgam spaces

Multi-window Gabor Frames in Amalgam Spaces

We show that multi-window Gabor frames with windows in the Wiener algebra W (L∞, `) are Banach frames for all Wiener amalgam spaces. As a by-product of our results we prove the canonical dual of a Gabor frame with a continuous generator in the Wiener algebra also belongs to this space. Our proofs are mostly based on recent noncommutative versions of Wiener’s 1/f lemma.

Gabor Analysis in Weighted Amalgam Spaces

Gabor frames {e2πinβ·xg(x− kα)}n,k∈Zd provide series representations not only of functions in L(R) but of the entire range of spaces M ν known as the modulation spaces. Membership of a function or distribution f in the modulation space is characterized by a sequence-space norm of the Gabor coefficients of f depending only on the magnitudes of those coefficients, and the Gabor series representat...

Generalized Frames in Hilbert Spaces

FUSION FRAMES IN HILBERT SPACES

Fusion frames are an extension to frames that provide a framework for applications and providing efficient and robust information processing algorithms. In this article we study the erasure of subspaces of a fusion frame.  

Approximately dual frames in Hilbert spaces and applications to Gabor frames

Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction. Bounds on the deviation from perfect reconstruction are obtained for approximately dual frames constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames,...