Characterization of Multiwavelets and MRA Wavelets in $$H^s(\mathbb {F})$$

Abstract

In the continuation of the paper [Pathak and Singh Wavelet in Sobolev space over local fields of positive characteristic, Int. J. of Wavelets Multi. Inf. Process,16 3 (2018)], we provide the characterizations of multiwavelets in Sobolev space over local fields of positive characteristic $$( H^s(\mathbb {F}))$$ by exploiting the theory of affine frame and quasi-affine frame and one example is presented. Further, the wavelets associated with MRA in $$ H^s(\mathbb {F})$$ are also characterized and an example is presented.