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.