On approximation by tight wavelet frames on the field of $p$-adic numbers

We discuss the problem on approximation by tight step wavelet frames on the field ${\mathbb{Q}}_p$ of $p$-adic numbers. Let $G_n=\{x={\sum }_{k=n}^{\mathrm{\infty }}{x}_k{p}^k\}$, $X$ be a set of characters. We define a step function $\lambda (\chi )$ that is constant on cosets $G_n^{\mathrm{\perp }}\setminus G_{n-1}^{\mathrm{\perp }}$ by equalities $\lambda (G_n^{\mathrm{\perp }}\setminus G_{n-1}^{\mathrm{\perp }})={\lambda }_n>0$ for which $\sum \frac{1}{{\lambda }_n}<\mathrm{\infty }$. We find the order of approximation of functions $f$ for which ${\int }_X\mathrm{\mid }\lambda (\chi )\widehat{f}(\chi ){\mathrm{\mid }}^{2}d\nu (\chi )<\mathrm{\infty }$