INVERSE SPECTRAL ANALYSIS FOR SINGULAR DIFFERENTIAL OPERATORS WITH MATRIX COEFFICIENTS

Let L-alpha be the Bessel operator with matrix coefficients defined on (0, infinity) by [GRAPHICS] 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.