A functional model of a class of symmetric semi-bounded operators

2023/11/02 by Μ. I. Belishev, Belishev, M. I., Sergey Simonov +1
Computer Science · Mathematics · #06B35 #34A55 #47A46 #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2311.01612

openalex publication_date 2023/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L₀ be a closed symmetric positive definite operator with nonzero defect indices n_±(L₀) in a separable Hilbert space \mathscr H. It determines a family of dynamical systems α^T, T>0, of the form \beginalign* & u"(t)+L₀^*u(t) = 0 && \rm in \mathscr H, 00. We show that under these assumptions the operator L₀ is unitarily equivalent to the minimal Schrödinger operator S₀=-D²+q in L₂(0,∞) with a smooth real-valued potential q, which is in the limit point case at infinity. It is also proved that S₀ provides a canonical wave model of L₀.

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