Frames and SingleWavelets for Groups

Let be a projective unitary representation of a discrete countable abelian group G on a separable Hilbert space which is associated to a cyclic generalized frame multiresolution analysis. We use Stone′s theorem and the theory of projection valued measure to analyze wandering frame collections. This yields a functional analytic method of constructing a wavelet from a generalized frame multiresolution analysis in term of the frame scaling vectors. If the set B of Bessel vectors for is dense in H, then for any vector x 2 H the analysis operator x makes sense as a densely defined operator from B to l2(G)-space.

کلیدواژه ها:

wavelet ، multiresolution analysis ، unitary group representation ، frame.