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DIFFERENTIAL GEOMETRY/PDE SEMINAR Wednesday, October 28, 2015 Padelford C-36 4PM–5PM Inverse spectral problems for elliptic operators

The subject of this talk concerns to the classical inverse spectral problem. This inverse problem can be formulated as follows: do the Dirichlet eigenvalues and the derivatives (which order?) of the normalized eigenfunctions at the boundary determine uniquely the coefficients of the corresponding differential operator? For operators of order two this type of theorem is called Borg-Levinson theorem. In the case of the Schrödinger operators the knowledge of the Dirichlet eigenvalues and the normal derivatives of the normalized eigenfunctions at the boundary uniquely determine unknown potential.