Zonal Schrödinger operators on the \(n\)-sphere: Inverse spectral problem and rigidity

DOI10.1007/BF02098276zbMath0798.34085WikidataQ61675419 ScholiaQ61675419MaRDI QIDQ1813314

David Gurarie

Publication date: 25 June 1992

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

inverse problemasymptotic expansionLaplace-Beltrami operatorspectral shiftsWeinstein cluster distribution measureszonal Schrödinger operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Inverse problems for PDEs (35R30) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Inverse scattering problems in quantum theory (81U40) Schrödinger operator, Schrödinger equation (35J10) Inverse problems involving ordinary differential equations (34A55) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items

Semiclassical eigenvalues and shape problems on surfaces of revolution, Completeness of the system of generalized eigenfunctions for a Bessel-type differential operator, Quantized Neumann problem, separable potentials on S n and the Lamè equation, Semiclassical approximation for Schrödinger operators on a two-sphere at high energy, Multiparameter averaging and inverse spectral problem for anharmonic oscillators in \(\mathbb{R}{}^ n\), On the eigenvalue asymptotics of Zonal Schrödinger operators in even metric and non-even metric, On the spectrum of the Schrödinger operator with a constant magnetic field plus a decreasing radial potential, Decay and Strichartz estimates in critical electromagnetic fields, Time decay of scaling invariant electromagnetic Schrödinger equations on the plane

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• QUANTIZATION