Geodesic
Chebyshev $C_0$-operator polynomials and their representation
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 38, Tome 376 (2010), pp. 64-87 Cet article a éte moissonné depuis la source Math-Net.Ru

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Certain estimates for the resolvent of a block-discrete Schrödinger operator with a constant diagonal perturbation are obtained. For that, the resolvent is represented in terms of the Chebychev polynomials of the (in general, unbounded) operator that represents a block of the perturbation. Bibl. – 12 titles. 
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V. A. Kostin; M. N. Nebolsina. Chebyshev $C_0$-operator polynomials and their representation. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 38, Tome 376 (2010), pp. 64-87. http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a3/

[1] V. A. Kostin, “K teoreme Solomyaka–Iosidy dlya analiticheskikh polugrupp”, Algebra i analiz, 11:1 (1999), 118–140 | MR | Zbl

[2] M. A. Krasnoselskii, Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966 | MR | Zbl

[3] M. G. Krein, “O spektre yakobievoi formy v svyazi s teoriei krutilnykh kolebanii valov”, Mat. sb., 40:4 (1933), 455–465 | Zbl

[4] S. G. Krein, Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967 | MR

[5] S. G. Krein, M. I. Khazan, “Differentsialnye uravneniya v banakhovom prostranstve”, Itogi nauki i tekhniki. Mat. analiz, 21, 1983, 130–264 | MR | Zbl

[6] M. A. Lavrentev, B. V. Shabat, Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1974 | MR

[7] G. Sege, Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[8] P. K. Suetin, Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1979 | MR | Zbl

[9] D. K. Faddeev, Lektsii po algebre, Nauka, M., 1984 | MR | Zbl

[10] D. K. Faddeev, “O svoistvakh matritsy obratnoi Khessenbergovoi”, Zap. nauchn. semin. LOMI, 111, 1981, 177–179 | MR | Zbl

[11] B. Simon, Orthogonal Polynomials on the Unit Circle, AMS Colloquium Series, Amer. Math. Soc., Providence, RI, 2005

[12] M. Zygmunt, “Matrix Chebyshev polynomials and continued fractions”, Linear Algebra and its Applications, 340:1–3 (2002), 155–168 | DOI | MR | Zbl