PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 69(83), pp. 5977 (2001) 

ON UNIFORM CONVERGENCE OF SPECTRAL EXPANSIONS ARISING BY SELFADJOINT EXTENSIONS OF AN ONEDIMENSIONAL SCHRÖDINGER OPERATORNebojsa L. Lazeti\'cMatemati\v cki fakultet, Beorad, YugoslaviaAbstract: 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 selfadjoint 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 (MSC2000): 47E05; 34L10 Full text of the article:
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