%0 Journal Article
%T Inverse spectral analysis for singular differential operators with matrix coefficients
%A Nour el Houda Mahmoud
%A Imen Yaich
%J Electronic Journal of Differential Equations
%D 2006
%I Texas State University
%X Let $L_alpha$ be the Bessel operator with matrix coefficients defined on $(0,infty)$ by $$ L_alpha U(t) = U''(t)+ {I/4-alpha^2over t^2}U(t), $$ where $alpha$ is a fixed diagonal matrix. The aim of this study, is to determine, on the positive half axis, a singular second-order differential operator of $L_alpha+Q$ kind and its various properties from only its spectral characteristics. Here $Q$ is a matrix-valued function. Under suitable circumstances, the solution is constructed by means of the spectral function, with the help of the Gelfund-Levitan process. The hypothesis on the spectral function are inspired on the results of some direct problems. Also the resolution of Fredholm's equations and properties of Fourier-Bessel transforms are used here.
%K Inverse problem
%K Fourier-Bessel transform
%K spectral measure
%K Hilbert-Schmidt operator
%K Fredholm's equation.
%U http://ejde.math.txstate.edu/Volumes/2006/16/abstr.html