Remarks on Schrödinger operators with singular matrix potentials

Abstract

In this paper, an asymmetric generalization of the Glazman-Povzner-Wienholtz theorem is proved for one-dimensional Schrödinger operators with strongly singular matrix potentials from the space $H_{loc}^{-1}(\mathbb{R}, \mathbb{C}^{m\times m})$. This result is new in the scalar case as well.

Key words: Glazman–Povzner–Wienholtz theorem, m-accretivity, complex-valued potential, distributional potential.

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Article Information

Title	Remarks on Schrödinger operators with singular matrix potentials
Source	Methods Funct. Anal. Topology, Vol. 19 (2013), no. 2, 161-167
MathSciNet	MR3098494
zbMATH	1289.34239
Milestones	Received 17/01/2013
Copyright	The Author(s) 2013 (CC BY-SA)

Authors Information

Vladimir Mikhailets
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Volodymyr Molyboga
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine 

Citation Example

Vladimir Mikhailets and Volodymyr Molyboga, Remarks on Schrödinger operators with singular matrix potentials, Methods Funct. Anal. Topology 19 (2013), no. 2, 161-167.

BibTex

@article {MFAT693,
    AUTHOR = {Mikhailets, Vladimir and Molyboga, Volodymyr},
     TITLE = {Remarks on Schrödinger operators with singular matrix potentials},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {19},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {161-167},
      ISSN = {1029-3531},
  MRNUMBER = {MR3098494},
 ZBLNUMBER = {1289.34239},
       URL = {http://mfat.imath.kiev.ua/article/?id=693},
}