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Inverse spectral problem for the 2-sphere Schrödinger operators with zonal potentials. (English) Zbl 0693.35124

From the author’s abstract: “Two basic problems of spectral theory of Schrödinger operators \(H=-\Delta +V(x)\) on the 2-sphere \(S_ 2\) are studied: (Direct problem) calculate large-k asymptotics of eigenvalue clusters \(\{\lambda_{kj}\}_ j\) in terms of the potential function V; (Inverse problem) recover V from asymptotics of eigenvalue clusters. We get an explicit solution of the inverse problem and establish local spectral rigidity for zonal potentials V.”
Reviewer: M.Chicco

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
35R30 Inverse problems for PDEs
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