$p$-Adic multiresolution analyses

Abstract

We study $p$-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating a MRA (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions and that all such scaling functions generate Haar MRA. We also suggest a method of constructing sets of wavelet functions and prove that any set of wavelet functions generates a $p$-adic wavelet frame.

17 pages

References in corpus (1)

• $p$-Adic multidimensional wavelets and their application to $p$-adic pseudo-differential operators

Cited by in corpus (1)

• p-Adic Mathematical Physics