Inverse problems for differential operators with singular boundary conditions

Abstract

Key words Differential operators, singular boundary conditions, inverse spectral problems MSC (2000) 34A55, 34B24, 34L40, 47E05Dedicated to the memory of F. V. Atkinson Singular boundary conditions are formulated for Sturm-Liouville operators having singularities and turning points at the end-points of the interval. For boundary-value problems with singular boundary conditions, inverse problems of spectral analysis are studied. We give formulations of the inverse problems both for the case of separated and non-separated singular boundary conditions. For each class of inverse problems we prove a uniqueness theorem and give a procedure for constructing the solution of the inverse problem.

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