p-Adic Scaling and Generalized Scaling Sets-Adic Scaling and Generalized Scaling Sets

This article aims to develop MRA theory along with wavelet theory through corresponding sets in L-2(Q(p)). Generalized scaling sets are important in wavelet theory because they determine (multi)wavelet sets. Although, the theory of scaling sets and generalized scaling sets on R and local fields of positive characteristics are already developed to some extent, but it is yet to be studied on local fields of zero characteristic like Q(p). This article presents necessary conditions for scaling sets with counting formulae for the elements in scaling sets, and characterization of generalized scaling sets with examples.