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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 $q\in W^{-1}_{2,\mathrm{unif}}(\mathbb R)$.


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Article Information

TitleSelf-adjointness of Schrödinger operators with singular potentials
SourceMethods Funct. Anal. Topology, Vol. 18 (2012), no. 2, 152-159
MathSciNet MR2978191
zbMATH 1262.47066
CopyrightThe 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 


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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},
}


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