ON INVERSE PROBLEM FOR SINGULAR STURM-LIOUVILLE OPERATOR FROM TWO SPECTRA

Abstract

In the paper an inverse problem by two given spectrum for second order differential operator with singularity of type delta/x(P) xp in zero point (where delta is a constant), is studied. It is well known that the two spectrum {lambda(n)} and {mu(n)} uniquely determine the potential function q (x) in a singular Sturm-Liouville equation defined on interval left perpendicular 0, pi right perpendicular. One of the aims of the paper is to prove the generalized degeneracy of the kernel of integral equation in inverse problem. In particular we obtain a new proof of Hochstadt's theorem concerning the structure of the difference (q) over tilde (x) - q (x)