Geodesic
Inverse spectral analysis for singular differential operators with matrix coefficients
Electronic journal of differential equations, Tome 2006 (2006)
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 
@article{EJDE_2006__2006__a189,
     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},
     year = {2006},
     volume = {2006},
     zbl = {1096.34007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a189/}
}
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AU  - Yaïch,  Imen
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%A Yaïch,  Imen
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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__a189/