Determination of an infinite non-self-adjoint Jacobi matrix from its generalized spectral function |
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Authors: | G. Sh. Guseinov |
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Affiliation: | 1. Lomonosov Moscow State University, USSR
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Abstract: | Restoration from the generalized spectral function of the equations $$b_0 y_0 + a_0 y_1 = lambda y_{0,} a_{n - 1} y_{n - 1} + b_n y_n + a_n y_{n + 1} = lambda y_{n,} n = 1,2,3,...,$$ wherea n and bn are arbitrary complex numbers,a n≠ 0 (n = o, i, 2,...), λ is a complex parameter, and {P n (λ)} 0 ∞ 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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