| On uniform convergence of spectral expansions and their derivatives for functions from $W_p^1$ |
| Nebojša L. Lažetić |
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 |
