Geodesic
Determination of an infinite non-self-adjoint Jacobi matrix from its generalized spectral function
Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 237-248

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Restoration from the generalized spectral function of the equations \begin{gather*} b_0y_0+a_0y_1=\lambda y_2, \\ a_{n-1}y_{n-1}+b_ny_n+a_ny_{n+1}=\lambda y_n,\quad n=1,2,3,\dots, \end{gather*} where $a_n$ and $b_n$ are arbitrary complex numbers, $a_n\ne0$ ($n=0,1,2,\dots$), $\lambda$ is a complex parameter, and $\{y_n\}_0^\infty$ infin is the required solution, is investigated. Necessary and sufficient conditions for solvability of the inverse problem are obtained, and the restoration procedure is described. 
@article{MZM_1978_23_2_a6,
     author = {G. Sh. Guseinov},
     title = {Determination of an infinite non-self-adjoint {Jacobi} matrix from its generalized spectral function},
     journal = {Matemati\v{c}eskie zametki},
     pages = {237--248},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a6/}
}
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G. Sh. Guseinov. Determination of an infinite non-self-adjoint Jacobi matrix from its generalized spectral function. Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 237-248. http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a6/