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In this work we prove that any pair of homogeneous dual multiwavelet frames of L 2 (R s ) constructed from a pair of refinable function vectors gives rise to a pair of nonhomogeneous dual multiwavelet frames and vice versa. We also prove that the Mixed Oblique Extension Principle characterizes dual multiwavelet frames. Our results extend recent characterizations of affine dual frames derived from scalar refinable functions obtained in [3].

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Let φ be a function in the Wiener amalgam space W ∞ (L 1 ) with a non-vanishing property in a neighborhood of the origin for its Fourier transform φ, τ = {τ n } n∈Z be a sampling set on R and V τ φ be a closed subspace of L 2 (R) containing all linear combinations of τ -translates of φ. In this paper we prove that every function f ∈ V τ φ is uniquely determined by and stably reconstructed from the sample set L τAs our reconstruction formula involves evaluating the inverse of an infinite matrix we consider a partial reconstruction formula suitable for numerical implementation. Under an additional assumption on the decay rate of φ we provide an estimate to the corresponding error.

ABSTRACT. We deal with the maximum Gibbs ripple of the sampling wavelet series of a discontinuous .function f at a point t ~ R, .for all possible values o.['a satisfying f (t) = ee.f (t -0) + (1 -cO.f (t + 0). For the Shannon wavelet series, we make a complete description of all ripples, .for any ot in [0,1]. We show that Meyer sampling series exhibit Gibbs Phenomenon.lor ce < 0.12495 and ct > 0.306853. We also give Meyer sampling formulas with maximum overshoots shorter than Shannon's for several et in [0,1].