The interior transmission problem is a boundary value problem that plays a basic role in inverse scattering theory but unfortunately does not seem to be included in any existing theory in partial differential equations.This paper presents old and new results for the interior transmission problem ,in particular its relation to inverse scattering theory and new results on the spectral theory asso...

We extend the classical spectral estimation problem to the infinitedimensional case and propose a new approach to this problem using the Boundary Control (BC) method. Several applications to inverse problems for partial differential equations are provided.

FOLLOING OUR PREVIOS PROJECT [1], WE ARE GOING TO PROVE THE EXISTENCE AND UNIQUENESS OF THE SOLUTION OF THE SPECTRAL PROBLEM IN THIS PROJECT.FIRST,WE HAVE PROVEN THE UNIQUENESS OF THE SOLUTION THEN TO PROVE THE EXISTRNCE WE CONSTENSS OF THE ADJOINT PROBLEM CORRESPONDING TO THIS SPECTRAL PROBLEM NEXT THE UNIQUESS OF THE ADJOINT PROBLEM IS THE EXISTENCE OF THE MAIN PROBLEM AS DISCUSSED BY[2] AND ...

Property C, that is, completeness of the set of products of some solutions to SturmLiouville equations is proved. Several uniqueness theorems for various inverse scattering problems are obtained in a very simple way with the help of property C. Two classical uniqueness results for inverse scattering problem on the half-axis and for the inverse spectral problem are proved in a very short new way...

in this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. furthermore, we obtain the zeros of eigenfunctions.

in this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. then a common general forward modeling for them is given and the corresponding inversion problem is presented. then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a baye...