We present two results dealing with dilation and perturbation properties of general frames, which generalize the works of several authors in the theory of discrete frames. We also study theâ€¦ (More)

We consider finite subsets Î› âŠ‚ Zn satisfying the extension property, i.e. the property that every collection {ck}kâˆˆÎ›âˆ’Î› of complex numbers which is positive-definite on Î› is the restriction to Î› âˆ’ Î›â€¦ (More)

A generalization of Mallatâ€™s classical multiresolution analysis, based on the theory of spectral pairs, was considered in two articles by Gabardo and Nashed. In this setting, the associatedâ€¦ (More)

Given a dÃ— d expansive dilation matrix D, a measurable set E âŠ‚ R d is called a Dt-dilation generator of Rd if Rd is tiled (modulo null sets) by the collection {(Dt)jE, j âˆˆ Z}. Our main goal in thisâ€¦ (More)

Let S be an aZ-periodic measurable subset of R with positive measure. It is well-known that the projection G(gÏ‡S , a, b) of a frame G(g, a, b) in L2(R) onto L2(S) is a frame for L2(S). However, whenâ€¦ (More)

The well-known density theorem for one-dimensional Gabor systems of the form (e2Jl'imbx g(x na)}m,nEZ, where g E L2(JR), states that a necessary and sufficient condition for the existence of such aâ€¦ (More)