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In this article we establish theory of semi-orthogonal Parseval waveletsassociated to generalized multiresolution analysis (GMRA) for the local fieldof positive characteristics (LFPC). By employing the properties of translationinvariant spaces on the core space of GMRA we obtain a characterization ofsemi-orthogonal Parseval wavelets in terms of consistency equation for LFPC. Asa consequence, we obtain a characterization of an orthonormal (multi)wavelet tobe associated with an MRA in terms of multiplicity function as well asdimension function of a (multi)wavelet. Further, we provide characterizationsof Parseval scaling functions, scaling sets and bandlimited wavelets togetherwith a Shannon type multiwavelet for LFPC.

Semi-orthogonal Parseval wavelets associated to GMRAs on local fields of positive characteristics