Abstract

We consider the global uniform convergence of spectral expansions and their derivatives, $\sum_{n=1}^{\infty}f_n\,u_n^{(j)}(x)$, $(j=0,1,2)$, 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

Keywords: Spectral expansion, uniform convergence, Schrödinger operator

MSC: 34L10, 47E05

Pages:  91--104     

Volume  56 ,  Issue  3$-$4 ,  2004