Determination of the infinite Jacobi matrix with respect to two-spectra |
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Authors: | G Sh Guseinov |
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Institution: | 1. Scientific-Research Computer Center of the Azerbaidzhan State University, USSR
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Abstract: | The inverse problem about two-spectra for the equation (1) $$\begin{gathered} b_0 y_0 + a_0 y_1 = \lambda y_0 , \hfill \\ a_{n - 1} y_{n - 1} + b_n y_n + a_n y_{n + 1} = \lambda y_n \left( {n = 1, 2, 3, ...} \right), \hfill \\ \end{gathered} $$ where {yn} 0 ∞ is the desired solution, λ is a complex parameter and $$a_n > 0, \operatorname{Im} b_n = 0 \left( {n = 0, 1 ,2, ...} \right)$$ is studied. Necessary and sufficient conditions for the solvability of the inverse problem about two-spectrafor Eq. (1) are established and also the procedure of reconstruction of the equation from its two-spectra is indicated. |
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