Geodesic
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 .

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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.
Classification : 47E05 34L10 
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     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},
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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/