Correction to: Inverse spectral theory for semiclassical Jaynes–Cummings systems

Semiclassical Inverse Spectral Theory for Singularities of Focus-focus Type

We prove, assuming that the Bohr-Sommerfeld rules hold, that the joint spectrum near a focus-focus critical value of a quantum integrable system determines the classical Lagrangian foliation around the full focus-focus leaf. The result applies, for instance, to ~-pseudodifferential operators, and to Berezin-Toeplitz operators on prequantizable compact symplectic manifolds.

Inverse Spectral Theory for One

New Approach to Inverse Spectral Theory

Symplectic inverse spectral theory for pseudodifferential operators

We prove, under some generic assumptions, that the semiclassical spectrum modulo O(~) 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.

Convergence theory for spectral deferred correction

In a recent article [2] Dutt, Greengard and Rohklin define two newmethods of deferred correction. Convergence for the the first method, using one step methods, has been proven in Hansen [8]. In this paper we augment the theory presented in [8] and use this to prove convergence for the second deferred correction method in [2] using linear k-step methods. This method has been known as Spectral De...