p-Adic multiresolution analyses

2008/10/07 by S. Albeverio, Albeverio, S., С. А. Евдокимов +3
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0810.1147

openalex publication_date 2008/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• p-Adic multiresolution analysis and wavelet frames
• p-Adic refinable functions and MRA-based wavelets
• p-Adic Haar multiresolution analysis
• p-Adic Haar multiresolution analysis and pseudo-differential operators
• Coincidence of the continuous and discrete p-adic wavelet transforms