Survey of the inverse spectral problem for the Notices of the ICCM
Steve Zelditch
TL;DR
This survey reviews recent developments and open problems in the inverse spectral problem, including rigidity results and scattering theory, providing an updated overview for mathematicians interested in spectral analysis.
Contribution
It offers an updated summary of inverse spectral problem research, highlighting new results and open questions since the previous survey.
Findings
Rigidity results for the ellipse
Phase shifts in scattering theory
Open problems in inverse oscillatory integrals
Abstract
This is an updated survey on the inverse spectral problem written for the Notices of the ICCM. It rapidly reviews some of the material in the previous survey of the same title (arXiv:math/0402356) and then discusses some relatively new results (rigidity results for the ellipse, phase shifts in scattering theory). The last section poses a number of open problems involving "inverse results for oscillatory integrals".
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum chaos and dynamical systems · Numerical methods in inverse problems