Oversampling of wavelet frames for real dilations
نویسندگان
چکیده
We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain of the core subspace.
منابع مشابه
Completeness of Orthonormal Wavelet Systems, for Arbitrary Real Dilations
It is shown that the discrete Calderón condition characterizes completeness of orthonormal wavelet systems, for arbitrary real dilations. That is, if a > 1, b > 0, and the system Ψ = {aψ(ax − bk) : j, k ∈ Z} is orthonormal in L(R), then Ψ is a basis for L(R) if and only if ∑ j∈Z |ψ̂(aξ)| = b for almost every ξ ∈ R. A new proof of the Second Oversampling Theorem is found, by similar methods.
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ورودعنوان ژورنال:
- J. London Math. Society
دوره 85 شماره
صفحات -
تاریخ انتشار 2012