We discuss the problem on approximation by tight step wavelet frames on the field $\mathbb{ Q}_p$ of $p$-adic numbers. Let $G_n=\{ x=\sum_{ k=n}^\infty x_k p^k\}$, $X$ be a set of characters. We define a step function $\lambda({ \chi})$ that is constant on cosets ${ G}_n^\bot\setminus{ G}_{ n-1}^\bot$ by equalities $\lambda ({ G}_n^\bot\setminus{ G}_{ n-1}^\bot)=\lambda_n>0$ for which $\sum\frac{ 1}{ \lambda_n}<\infty$. We find the order of approximation of functions $f$ for which $\int_X|\lambda( { \chi})\hat{ f}(\chi)|^2d\nu(\chi)<\infty$
Categories: math.NT math.FA