Approximation by refinement masks

Abstract

In the paper we design a Parseval wavelet frame with a compact support. The corresponding refinement mask uniformly approximates an arbitrary continuous periodic function $f$, $f(0)=1$, $|f(x){|}^2+|f(x+\pi ){|}^2\le 1$. The refinable function has stable integer shifts.

arXiv comment6 pages. arXiv admin note: substantial text overlap with arXiv:2207.08252