On Uniform Convergence of Spectral Expansions and Their Derivatives for Functions From Wp1

Nebojša_L. Lažetić

We consider the global uniform convergence of spectral expansions and their derivatives, $ \sum_{n=1}^{\infty}f_nu_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