Abstract:
This thesis address some problems on frames and their generalizations viz Hilbert space valued Gabor frames and Hilbert-Schmidt frames. Mainly, we analyze Gabor frames on amalgam spaces, obtain solution of a Feichtinger problem and establish Balian–Low type theorems on L2(C). Thesis is divided into six chapters. In Chapter 1, we give a brief introduction of frame theory, discuss some well-known results, basic definitions and provide a literature survey. In Chapter 2, we prove the convergence of Gabor expansions to identity operator in the operator norm as well as weak* sense on W(Lp,Lq) as the sampling density tends to infinity. Using it we show the validity of the Janssen’s representation and the Wexler-Raz biorthogonality condition for Gabor frame operator on W(Lp,Lq).
