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- W3140638676 abstract "Given L, N, M ∈ N and an NZ-periodic set S in Z, let l2(S) be the closed subspace of l2(Z) consisting of sequences vanishing outside S. For f = { fl : 0≤l≤L-1 }l2(Z), we denote by G(f, N, M) the Gabor system generated by f, and by L(f, N, M) the closed linear subspace generated by G(f, N, M). This paper addresses density results, frame conditions for a Gabor system G(g, N, M) in l2(S), and Gabor duals of the form G(a, N, M) in some L(h, N, M) for a frame G(g, N, M) in l2(S) (so-called oblique duals). We obtain a density theorem for a Gabor system G(g, N, M) in l2(S), and show that such condition is suficient for theexistence of g={XE1:0≤l≤L-1} with G(g,N,m) We characterize g with G(g,N,m) being respectively a frame for L(g,N,m) being a tight frame for l2(S).and G(h, N, M ) in L(h, N, M ), we establish a criterion for the existence of an oblique Gabor dual of g in L(h, N, M), study the uniqueness of oblique Gabor dual, and derive an explicit expression of a class of oblique Gabor duals (among which the one with the smallest norm is obtained). Some examples are also provided." @default.
- W3140638676 created "2021-04-13" @default.
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- W3140638676 date "2011-01-01" @default.
- W3140638676 modified "2023-09-28" @default.
- W3140638676 title "Multi-window Gabor frames and oblique Gabor duals on discrete periodic sets" @default.
- W3140638676 hasPublicationYear "2011" @default.
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