On uniform convergence of spectral expansions and their derivatives for functions from $W_p^1$

Abstract

We consider the global uniform convergence of spectral expansions and their derivatives, $\sum_{n=1}^{ınfty}f_n\,u_n^{(j)}(x)$, $(j=0,1,2)$, arising by an arbitrary one-dimensional self-adjoint Schrödinger operator, defined on a bounded interval $G\subset\Bbb R$. We establish the absolute and uniform convergence on $\overline G$ of the series, supposing that $f$ belongs to suitable defined subclasses of $W_p^{(1+j)}(G)$ $(1<p\le 2)$. Also, some convergence rate estimates are obtained.