Abstract
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 subspace V0 of L2(K) has a frame, a collection of translates of the scaling function φ of the form φ(·-u(k)):k∈N0, where N0 is 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 field K of positive characteristic using the shift-invariant space theory.
Highlights
Multiresolution analysis is considered as the heart of wavelet theory
We present a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shift-invariant spaces
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
Summary
Multiresolution analysis is considered as the heart of wavelet theory. The concept of multiresolution analysis provides a natural framework for understanding and constructing discrete wavelet systems. Shah and Abdullah [12] have introduced the notion of nonuniform multiresolution analysis on local field K of positive characteristic and Journal of Operators obtained the necessary and sufficient condition for a function φ to generate a nonuniform multiresolution analysis on local fields. More results in this direction can be found in [13, 14] and the references therein.
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