On compact perturbations of finite-zone Jacobi operators
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 37, Tome 366 (2009), pp. 84-101 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a bounded Jacobi operator (a discrete analog of the Sturm–Liouville operator on the semi-axis), the compactness of a perturbation is investigated. The perturbation is produced by a change of the spectral measure (essential spectrum stays unchanged). Bibl. – 21 titles.
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A. A. Kononova. On compact perturbations of finite-zone Jacobi operators. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 37, Tome 366 (2009), pp. 84-101. http://geodesic.mathdoc.fr/item/ZNSL_2009_366_a5/

[1] A. I. Aptekarev, “Asimptoticheskie svoistva mnogochlenov, ortogonalnykh na sisteme konturov, i periodicheskie dvizheniya tsepochek Toda”, Matem. sb., 125(167):2(10) (1984), 231–258 | MR | Zbl

[2] N. I. Akhiezer, Klassicheskaya problema momentov, 1961

[3] N. I. Akhiezer, “Ob ortogonalnykh mnogochlenakh na neskolkikh intervalakh”, Dokl. AN SSSR, 134:1 (1960), 9–12 | Zbl

[4] B. A. Dubrovin, “Teta-funktsii i nelineinye uravneniya”, UMN, 36:2(218) (1981), 11–80 | MR | Zbl

[5] V. A. Kalyagin, A. A. Kononova, “Ob asimptotike mnogochlenov, ortogonalnykh na sisteme dug, po mere, imeyuschei diskretnuyu chast”, Algebra i Analiz, 21:2 (2009), 71–91 | MR | Zbl

[6] V. A. Kalyagin, A. A. Kononova, “O kompaktnykh vozmuscheniyakh predelno-periodicheskogo operatora Yakobi”, Matem. zametki, 86:6 (2009), 845–858 | DOI | MR | Zbl

[7] E. M. Nikishin, V. N. Sorokin, Ratsionalnye approksimatsii i ortogonalnost, Nauka, M., 1988 | MR | Zbl

[8] E. A. Rakhmanov, “Ob asimptotike otnosheniya ortogonalnykh mnogochlenov”, Matem. sb., 103(145):2(6) (1977), 237–252 | MR | Zbl

[9] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, v. 4, Analiz operatorov, Mir, M., 1977

[10] Yu. Ya. Tomchuk, “Ortogonalnye mnogochleny na sisteme intervalov chislovoi osi”, Zapiski mekh.-mat. f-ta Kharkovskogo matem. obschestva, 29:4 (1963), 93–128

[11] N. G. Chebotarev, Teoriya algebraicheskikh funktsii, Gostekhizdat, M., 1948

[12] A. I. Aptekarev, V. Kaliaguine, W. Van Assche, “Criterion for the resolvent set of nonsymmetric tridiagonal operators”, Proc. Amer. Math. Soc., 123 (1995), 2423–2430 | DOI | MR | Zbl

[13] B. Beckermann, “Complex Jacobi matrices”, J. Comput. Appl. Math., 127 (2001), 17–65 | DOI | MR | Zbl

[14] B. Beckermann, V. A. Kaliaguine, A. A. Kononova, Mass points and compact perturbation of finite zone Jacobi operator, Preprint

[15] D. Damanik, R. Killip, B. Simon, Perturbations of orthogonal polynomials with periodic recursion coefficients, arXiv: 0702388 | MR

[16] S. Denisov, “On Rakhmanov's theorem for Jacobi matrices”, Proc. Amer. Math. Soc., 132 (2004), 847–852 | DOI | MR | Zbl

[17] S. Denisov, B. Simon, “Zeros of orthogonal polynomials on the real line”, J. Approx. Theory, 121 (2003), 357–364 | DOI | MR | Zbl

[18] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966 | MR | Zbl

[19] F. Peherstorfer, P. Yuditskii, “Asymptotic behavior of polynomials orthonormal on a homogeneous set”, J. d'Analyse Mathématique, 89:1 (2003), 113–154 | DOI | MR | Zbl

[20] C. Remling, The absolutely continuous spectrum of Jacobi matrices, arXiv: 0706.1101

[21] H. Widom, “Extremal Polynomials Associated with a System of Curves and Arcs in the Complex Plane”, Adv. in Mathem., 3:2 (1969), 127–232 | DOI | MR | Zbl