Conditions for discreteness of the spectrum to multi-dimensional\n Schr "odinger operator

2019/06/05 by Leonid Zelenko, Zelenko, Leonid
Mathematics · #47B25 #47D08 #90C10 #90C27 #91A12 #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Primary 47F05 #Secondary 81Q10 #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #\\35P05

paper · pdf · doi:10.48550/arxiv.1906.02186

openalex publication_date 2019/06/05 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

This work is a continuation of our previos paper citeZel1, where for the\nthe Schr "odinger operator H=-\Δ+ V( e)\⋅ (V( e)\≥ 0), acting in\nthe space L₂( R^d) ,(d\≥ 3), some constructive sufficient conditions for\ndiscreteness of its spectrum have been obtained on the base of well known Mazya\n-Shubin criterion and an optimization problem for a set function. Using a it\ncapacitary strong type inequality of David Adams, the concept of it base\npolyhedron for the harmonic capacity and some properties of Choquet integral\nby this capacity, we obtain more general sufficient conditions for discreteness\nof the spectrum of H in terms of a repeated nonincreasing rearrangement of\nthe function Y( e, bt)=\√(V( e)) frac1| e- bt|^d-2\√(V( bt)) on\ncubes that are going to infinity.\n

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