Geodesic
Asymptotics of Eigenvalues for a Class of Jacobi Matrices with Limiting Point Spectrum
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 449-462 
É. A. Tur. Asymptotics of Eigenvalues for a Class of Jacobi Matrices with Limiting Point Spectrum. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 449-462. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a13/
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     title = {Asymptotics of {Eigenvalues} for a {Class} of {Jacobi} {Matrices} with {Limiting} {Point} {Spectrum}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a13/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study a class of Jacobi matrices with very rapidly decreasing weights. It is shown that the Weyl function (the matrix element of the resolvent of the operator) for the class under study can be expressed as the ratio of two entire transcendental functions of order zero. It is shown that the coefficients in the expansion of these functions in Taylor series are proportional to the generating functions of the number of integral solutions defined by certain Diophantine equations. An asymptotic estimate for the eigenvalues is obtained.

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