Inverse problems in spectral geometry

Abstract

In this survey we review positive inverse spectral and inverse resonant results for the following kinds of problems: Laplacians on bounded domains, Laplace-Beltrami operators on compact manifolds, Schrödinger operators, Laplacians on exterior domains, and Laplacians on manifolds which are hyperbolic near infinity.

26 pages

References in corpus (6)

• A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition
• Inverse Spectral Problem for Schrödinger Operators
• Resonant uniqueness of radial semiclassical Schrodinger operators
• A Fulling-Kuchment theorem for the 1D harmonic oscillator
• Semiclassical Spectral Invariants for Schrödinger Operators
• $C^{\infty }$ spectral rigidity of the ellipse

Cited by in corpus (9)

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• A Fulling-Kuchment theorem for the 1D harmonic oscillator
• Quantum footprints of Liouville integrable systems
• Asymptotic Lattices, Good Labellings, and the Rotation Number for Quantum Integrable Systems
• Hearing the shape of a triangle
• Triple Products of Eigenfunctions and Spectral Geometry