Geodesic
Titchmarsh--Weyl formula for the spectral density of a class of Jacobi matrices in the critical case
Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 2, pp. 21-43

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We consider a class of Jacobi matrices with unbounded entries in the so-called critical (double root, Jordan block) case. We prove a formula which relates the spectral density of a matrix to the asymptotics of orthogonal polynomials associated with it. 
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     author = {S. N. Naboko and S. A. Simonov},
     title = {Titchmarsh--Weyl formula for the spectral density of a class of {Jacobi} matrices in the critical case},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     number = {2},
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S. N. Naboko; S. A. Simonov. Titchmarsh--Weyl formula for the spectral density of a class of Jacobi matrices in the critical case. Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 2, pp. 21-43. http://geodesic.mathdoc.fr/item/FAA_2021_55_2_a2/