Mahmoud, Nour el HoudaYaich, Imen2021-07-142021-07-142006-02-02Mahoud, N. H., & Yaïch, I. (2006). Inverse spectral analysis for singular differential operators with matrix coefficients. <i>Electronic Journal of Differential Equations, 2006</i>(16), pp. 1-19.1072-6691https://hdl.handle.net/10877/13889Let Lα be the Bessel operator with matrix coefficients defined on (0, ∞) by LαU(t) = U″ (t) + I/4 - α2 / t2 U(t), where α 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 Lα + 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.Text19 pages1 file (.pdf)enAttribution 4.0 InternationalInverse problemFourier-Bessel transformSpectral measureHilbert-Schmidt operatorFredholm's equationArticle