Self-adjointness of Schroedinger operators with singular potentials

2011/11/03 by Rostyslav O. Hryniv, Hryniv, Rostyslav O., Yaroslav V. Mykytyuk +1 · 3 citations
Mathematics · #34L05 (Primary) #34L40 #47A05 #47B25 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #math.FA #math.SP #msc:34L05 #msc:34L40 #msc:47A05 #msc:47B25

paper · pdf · doi:10.48550/arxiv.1111.0809

AMS-LaTeX, 8 pages; essentially revised; to appear in Meth. Funct. Anal. Topol. 18 (2012), no. 2

arxiv created 2012/03/21 · arxiv updated 2012/03/23

Abstract

We study one-dimensional Schroedinger operators S with real-valued distributional potentials q in W^-1_2,loc(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,unif(R).

Cited by

• Uniqueness problem for accretive Schrödinger operators with complex singular coefficients
• A generalized Birman-Schwinger principle and applications to one-dimensional Schrödinger operators with distributional potentials
• Schrödinger operators with complex singular potentials

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