Learn More
The Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a(More)
Let A 1 and A 2 be expansive dilations, respectively, on R n and R m. Let A ≡ (A 1 , A 2) and A p (A) be the class of product Muckenhoupt weights on R n × R m for p ∈ (1, ∞]. When p ∈ (1, ∞) and w ∈ A p (A), the authors characterize the weighted Lebesgue space L p w (R n × R m) via the anisotropic Lusin-area function associated with A. When p ∈ (0, 1], w ∈(More)
Let S be a shift-invariant subspace of L 2 (R n) defined by N generators and suppose that its length L, the minimal number of generators of S, is smaller than N. Then we show that at least one reduced family of generators can always be obtained by a linear combination of the original generators, without using translations. In fact, we prove that almost(More)
Using the range function approach to shift invariant spaces in L 2 (R n) we give a simple characterization of frames and Riesz families generated by shifts of a countable set of generators in terms of their behavior on subspaces of l 2 (Z n). This in turn gives a simpliied approach to the analysis of frames and Riesz families done by Gramians and dual(More)