Geodesic
Inverse spectral analysis for singular differential operators with matrix coefficients
Electronic Journal of Differential Equations, Tome 2006 (2006).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $$ L_\alpha U(t) = U''(t)+ {I/4-\alpha^2\over t^2}U(t), $$ 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.
Classification : 45Q05, 45B05, 45F15, 34A55, 35P99
Keywords: inverse problem, Fourier-Bessel transform, spectral measure, Hilbert-Schmidt operator, Fredholm's equation 
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     author = {El Houda Mahmoud, Nour and Ya{\"\i}ch, Imen},
     title = {Inverse spectral analysis for singular differential operators with matrix coefficients},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a89/}
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El Houda Mahmoud, Nour; Yaïch, Imen. Inverse spectral analysis for singular differential operators with matrix coefficients. Electronic Journal of Differential Equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a89/