φ-factorable operators and Weyl-Heisenberg frames on LCA groups

φ-factorable operators and weyl-heisenberg frames on lca groups

φ-factorable operators and weyl-heisenberg frames on lca groups

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A Necessary Condition for Weyl-Heisenberg Frames

Perturbations of Weyl-heisenberg Frames

for all f ∈ H . The constant A (respectively, B) is a lower (resp. upper) frame bound for the frame. One of the most important frames for applications, especially signal processing, are the Weyl-Heisenberg frames. For g ∈ L(R) we define the translation parameter a > 0 and the modulation parameter b > 0 by: Embg(t) = e , Tnag(t) = g(t− na). For g ∈ L(R) and a, b > 0, we say for short that (g, a,...

Classifying Tight Weyl-heisenberg Frames

Lattice Tiling and the Weyl-Heisenberg Frames

Let L and K be two full rank lattices in R. We prove that if v(L) = v(K), i.e. they have the same volume, then there exists a measurable set Ω such that it tiles R by both L and K. A counterexample shows that the above tiling result is false for three or more lattices. Furthermore, we prove that if v(L) ≤ v(K) then there exists a measurable set Ω such that it tiles by L and packs by K. Using th...