HOCHSTADT'S RESULTS FOR INVERSE STURM{LIOUVILLE PROBLEMS WITH FINITE NUMBER OF TRANSMISSION AND PARAMETER DEPENDENT BOUNDARY CONDITIONS

HOCHSTADT'S RESULTS FOR INVERSE STURM{LIOUVILLE PROBLEMS WITH FINITE NUMBER OF TRANSMISSION AND PARAMETER DEPENDENT BOUNDARY CONDITIONS

M. Shahriari

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Abstract

This paper deals with the boundary value problem involving the di erential equation y00 + qy =  y; subject to the parameter dependent boundary conditions with  nite number of transmission conditions. The potential function q 2 L2(0;  ) is real and   is a spectral parameter. We develop the Hochstadt's results based on the transformation operator for inverse Sturm{Liouville problem when there are  nite number of transmission and parameter dependent boundary conditions. Furthermore, we establish a formula for q(x) ~q(x) in the  nite interval [0;  ], where q(x) and ~q(x) are analogous functions.

Keywords

Inverse Sturm{Liouville problem, Mittag{Le er expansion, discontinuous conditions, transformation operator, Green's function.