Scientific-Research Computer Center of the Azerbaidzhan State University
Abstract:
The inverse problem about two-spectra for the equation
\begin{gather*}
b_0y_0+a_0y_1=\lambda y_0,\\
a_{n-1}y_{n-1}+b_ny_n+a_ny_{n+1}=\lambda y_n\qquad (n=1,2,3,\dots),\tag{1}
\end{gather*}
where $\{y_n\}_0^\infty$ is the desired solution, $\lambda$ is a complex parameter and
$$
a_n>0, \quad\mathrm{Im}\,b_n=0,\qquad (n=0,1,2,\dots)
$$
is studied. Necessary and sufficient conditions for the solvability of the inverse problem
about two-spectra for Eq. (1) are established and also the procedure of reconstruction of the equation from its two-spectra is indicated.
Fulltext:
PDF file (1345 kB)
