Semi-orthogonal Parseval Wavelets Associated with GMRAs on Local Fields of Positive Characteristic
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In this article, we establish theory of semi-orthogonal Parseval wavelets associated with generalized multiresolution analysis (GMRA) for local fields of positive characteristics (LFPC) and obtain their characterization in terms of consistency equation. As a consequence, we obtain a characterization of an orthonormal (multi)wavelet associated with an MRA in terms of multiplicity function as well as dimension function. Further, we provide characterizations of Parseval scaling functions, scaling sets and bandlimited wavelets together with a Shannon-type multiwavelet. Some examples of such wavelets are also produced for LFPC.
KeywordsLocal fields translation invariant spaces multiplicity function semi-orthogonal Parseval wavelets bandlimited wavelets
Mathematics Subject Classification42C40 42C15 43A70 11S85
The authors would like to thank all the anonymous reviewers for providing fruitful suggestions to improve the presentation of this article. The first and second authors were supported by NBHM (DAE) grant-14723 and TEQIP-III, NPIU (MHRD), respectively, during the revision of manuscript.
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