We present a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shift-invariant spaces. In contrast to the standard setting, the associated subspaceV0ofL2(K)has a frame, a collection of translates of the scaling functionφof the formφ(·-u(k)):k∈N0, whereN0is the set of nonnegative integers. We investigate certain properties of multiresolution subspaces which provides the quantitative criteria for the construction of frame multiresolution analysis (FMRA) on local fields of positive characteristic. Finally, we provide a characterization of wavelet frames associated with FMRA on local fieldKof positive characteristic using the shift-invariant space theory.
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