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Isaac Newton Institute for Mathematical Sciences

Pollution-free methods for finding eigenvalues in the gaps of the continuous spectrum

22nd May 2007

Author: Michael Levitin (Heriot-Watt, Edinburgh)

Abstract

We describe a universal non-variational approach allowing to find numerically the eigenvalues of a self-adjoint operator in the gaps of essential spectrum. The method does not produce spurious eigenvalues and gives two-sided a posteriori error estimates. As an illustration, we discuss a periodic Schroedinger operator perturbed by a compact potential.