Geodesic
The Direct and Inverse Spectral Problems for some Banded Matrices
Serdica Mathematical Journal, Tome 37 (2011) no. 1, pp. 9-24.

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In this paper we introduced a notion of the generalized spectral function for a matrix J = (gk,l)k,l = 0 Ґ, gk,l О C, such that gk,l = 0, if |k-l | > N; gk,k+N = 1, and gk,k-N № 0. Here N is a fixed positive integer. The direct and inverse spectral problems for such matrices are stated and solved. An integral representation for the generalized spectral function is obtained.
Keywords: Banded Matrix, Spectral Function, Polynomials 
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Zagorodnyuk, S. M. The Direct and Inverse Spectral Problems for some Banded Matrices. Serdica Mathematical Journal, Tome 37 (2011) no. 1, pp. 9-24. http://geodesic.mathdoc.fr/item/SMJ2_2011_37_1_a1/