Convergence of Subdivision Schemes and Smoothness of Refinable Functions on p-adic Fields

TL;DR

This paper systematically studies p-adic refinement equations and subdivision schemes, characterizing their convergence and smoothness properties, and establishing connections with spectral radii of associated operators.

Contribution

It provides a comprehensive analysis of p-adic subdivision schemes, linking convergence and smoothness to spectral radii, a novel approach in p-adic analysis.

Findings

Lq-convergence characterized by q-norm joint spectral radii

Smoothness of complex-valued functions on Qp analyzed

Framework established for p-adic refinement equations

Abstract

A systematic and comprehensive study of p-adic refinement equations and subdivision scheme associated with a finitely supported refinement mask are carried out in this paper. The Lq -convergence of the subdivision scheme is characterized in terms of the q-norm joint spectral radii of a collection of operators associated with the refinement mask. Also, the smoothness of complex-valued functions on Qp is investigated.