On Uniform Convergence of Spectral Expansions Arising by Self-adjoint Extensions of an One-dimensional SchrÖdinger Operator
Publications de l'Institut Mathématique, _N_S_69 (2001) no. 83, p. 59
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
We consider the problem of global uniform convergence of spectral
expansions and their derivatives,
$\sum\limits_{n=1}^{\infty}f_n\,u^{(j)}_n(x)$ ($j=0,1,\dots$),
generated by arbitrary self-adjoint extensions of the operator
$\mathcal L(u)(x) = - u''(x) + q(x)\,u(x)$ with discrete spectrum, for
functions from the classes $H_p^{(k,\alpha)}(G)$
($k\in \mathbb N$, $\alpha\in (0,1]$) and $W^{(k)}_p(G)$ ($1\le p\le 2$),
where $G$ is a finite interval of the real axis. Two theorems giving
conditions on functions $q(x)$, $f(x)$ which are sufficient for the
absolute and uniform convergence on $\olG$ of the mentioned
series, are proved. Also, some convergence rate estimates are obtained.
@article{PIM_2001_N_S_69_83_a8,
author = {Neboj\v{s}a L. La\v{z}eti\'c},
title = {On {Uniform} {Convergence} of {Spectral} {Expansions} {Arising} by {Self-adjoint} {Extensions} of an {One-dimensional} {Schr\"Odinger} {Operator}},
journal = {Publications de l'Institut Math\'ematique},
pages = {59 },
publisher = {mathdoc},
volume = {_N_S_69},
number = {83},
year = {2001},
zbl = {1004.47029},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_2001_N_S_69_83_a8/}
}
TY - JOUR AU - Nebojša L. Lažetić TI - On Uniform Convergence of Spectral Expansions Arising by Self-adjoint Extensions of an One-dimensional SchrÖdinger Operator JO - Publications de l'Institut Mathématique PY - 2001 SP - 59 VL - _N_S_69 IS - 83 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/PIM_2001_N_S_69_83_a8/ LA - en ID - PIM_2001_N_S_69_83_a8 ER -
%0 Journal Article %A Nebojša L. Lažetić %T On Uniform Convergence of Spectral Expansions Arising by Self-adjoint Extensions of an One-dimensional SchrÖdinger Operator %J Publications de l'Institut Mathématique %D 2001 %P 59 %V _N_S_69 %N 83 %I mathdoc %U http://geodesic.mathdoc.fr/item/PIM_2001_N_S_69_83_a8/ %G en %F PIM_2001_N_S_69_83_a8
Nebojša L. Lažetić. On Uniform Convergence of Spectral Expansions Arising by Self-adjoint Extensions of an One-dimensional SchrÖdinger Operator. Publications de l'Institut Mathématique, _N_S_69 (2001) no. 83, p. 59 . http://geodesic.mathdoc.fr/item/PIM_2001_N_S_69_83_a8/