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# Self-adjointness of Schrödinger operators with singular potentials

### Abstract

We study one-dimensional Schrödinger operators $S$ with real-valued distributional potentials $q$ in $W^{-1}_{2,\mathrm{loc}}(\mathbb R)$ and prove an extension of the Povzner-Wienholtz theorem on self-adjointness of bounded below $S$ thus providing additional information on its domain. The results are further specified for $q\in W^{-1}_{2,\mathrm{unif}}(\mathbb R)$.

### Article Information

 Title Self-adjointness of Schrödinger operators with singular potentials Source Methods Funct. Anal. Topology, Vol. 18 (2012), no. 2, 152-159 MathSciNet MR2978191 zbMATH 1262.47066 Copyright The Author(s) 2012 (CC BY-SA)

### Authors Information

Rostyslav O. Hryniv
Institute for Applied Problems of Mechanics and Mathematics, 3b~Naukova, Lviv, 79601, Ukraine

Yaroslav V. Mykytyuk
Lviv National University, 1 Universytets'ka, Lviv, 79602, Ukraine

### Citation Example

Rostyslav O. Hryniv and Yaroslav V. Mykytyuk, Self-adjointness of Schrödinger operators with singular potentials, Methods Funct. Anal. Topology 18 (2012), no. 2, 152-159.

### BibTex

@article {MFAT619,
AUTHOR = {Hryniv, Rostyslav O. and Mykytyuk, Yaroslav V.},
TITLE = {Self-adjointness of Schrödinger operators with singular potentials},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {18},
YEAR = {2012},
NUMBER = {2},
PAGES = {152-159},
ISSN = {1029-3531},
MRNUMBER = {MR2978191},
ZBLNUMBER = {1262.47066},
URL = {http://mfat.imath.kiev.ua/article/?id=619},
}