One-dimensional Schrödinger operators with δ'-interactions on a set of Lebesgue measure zero

2011/12/12 by Johannes F. Brasche, Brasche, Johannes F., Л. П. Нижник +2
Computer Science · Mathematics · #47A55 #47A70 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories #math.FA #math.SP #msc:47A55 #msc:47A70

paper · pdf · doi:10.48550/arxiv.1112.2545

22 pages

arxiv created 2011/12/12 · openalex publication_date 2011/12/12 · arxiv updated 2011/12/13 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We give an abstract definition of a one-dimensional Schrödinger operator with δ'-interaction on an arbitrary set~Γ of Lebesgue measure zero. The number of negative eigenvalues of such an operator is at least as large as the number of those isolated points of the set~Γ that have negative values of the intensity constants of the δ'-interaction. In the case where the set~Γ is endowed with a Radon measure, we give constructive examples of such operators having an infinite number of negative eigenvalues.

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