Geodesic
The direct and inverse problem of spectral analysis for five-diagonal simmetric matrices. I
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (1998) no. 3, pp. 182-202 Cet article a éte moissonné depuis la source Math-Net.Ru

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The five-diagonal simmetric matrices of finite order are considered. The matrix-valued spectral measure associated with the eigenvector expansion is introduced. The necessary and sufficient conditions for a matrix-valued measure to be the spectral measure of such a matrix are obtained. The method of reconstruction of the five-diagonal matrices is obtained. 
@article{JMAG_1998_5_3_a3,
     author = {M. A. Kudryavtsev},
     title = {The direct and inverse problem of spectral analysis for five-diagonal simmetric {matrices.~I}},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {182--202},
     year = {1998},
     volume = {5},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1998_5_3_a3/}
}
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M. A. Kudryavtsev. The direct and inverse problem of spectral analysis for five-diagonal simmetric matrices. I. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (1998) no. 3, pp. 182-202. http://geodesic.mathdoc.fr/item/JMAG_1998_5_3_a3/