Symplectic inverse spectral theory for pseudodifferential operators

Details Symplectic inverse spectral theory for pseudodifferential operators Symplectic inverse spectral theory for pseudodifferential operators

2008-08-21

arxiv.org/abs/0808.2862v1

Mathematics

Spectral Theory

23 pages

Scientific paper

We prove, under some generic assumptions, that the semiclassical spectrum
modulo O(h^2) of a one dimensional pseudodifferential operator completely
determines the symplectic geometry of the underlying classical system. In
particular, the spectrum determines the hamiltonian dynamics of the principal
symbol.

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