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
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 },
year = {2001},
volume = {_N_S_69},
number = {83},
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 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 %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/