On the Negative Spectrum of One-Dimensional Schr "odinger Operators with\n Point Interactions

2009/03/06 by Nataly Goloschapova, Goloschapova, Nataly, Л. Л. Оридорога +1
Computer Science · Mathematics · #34L40 #47A10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0903.1180

openalex publication_date 2009/03/06 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We investigate negative spectra of 1--D Schr "odinger operators with\n\δ- and \δ'-interactions on a discrete set in the framework of a\nnew approach. Namely, using technique of boundary triplets and the\ncorresponding Weyl functions, we complete and generalize the results of S.\nAlbeverio and L. Nizhnik. For instance, we propose the algorithm for\ndetermining the number of negative squares of the operator with\n\δ-interactions. We also show that the number of negative squares of the\noperator with \δ'-interactions equals the number of negative strengths.\n

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