Inverse Spectral Theory for Perturbed Torus

Remarks on the inverse spectral theory for singularly perturbed operators

Let A be an unbounded from above self-adjoint operator in a separable Hilbert space H and EA(·) its spectral measure. We discuss the inverse spectral problem for singular perturbations à of A (à and A coincide on a dense set in H). We show that for any a ∈ R there exists a singular perturbation à of A such that à and A coincide in the subspace EA((−∞, a))H and simultaneously à has an additional...

On Inverse Spectral Theory for Singularly Perturbed Operators: Point Spectrum

Inverse Spectral Theory for One

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.

Inverse spectral problems for Sturm-Liouville operators with transmission conditions

Abstract: This paper deals with the boundary value problem involving the differential equation                      -y''+q(x)y=lambda y                                 subject to the standard boundary conditions along with the following discontinuity conditions at a point              y(a+0)=a1y(a-0),    y'(a+0)=a2y'(a-0)+a3y(a-0).  We develop the Hochestadt-Lieberman’s result for Sturm-Lio...