MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
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

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Keywords: Spectral expansion, uniform convergence, Schrödinger operator

MSC: 34L10, 47E05

Pages:  91--104     

Volume  56 ,  Issue  3$-$4 ,  2004