Abstract:
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.
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