Approximation by refinement masks

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