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 
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/
@article{ZNSL_2010_376_a3,
     author = {V. A. Kostin and M. N. Nebolsina},
     title = {Chebyshev $C_0$-operator polynomials and their representation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {64--87},
     year = {2010},
     volume = {376},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a3/}
}
TY  - JOUR
AU  - V. A. Kostin
AU  - M. N. Nebolsina
TI  - Chebyshev $C_0$-operator polynomials and their representation
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2010
SP  - 64
EP  - 87
VL  - 376
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a3/
LA  - ru
ID  - ZNSL_2010_376_a3
ER  - 
%0 Journal Article
%A V. A. Kostin
%A M. N. Nebolsina
%T Chebyshev $C_0$-operator polynomials and their representation
%J Zapiski Nauchnykh Seminarov POMI
%D 2010
%P 64-87
%V 376
%U http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a3/
%G ru
%F ZNSL_2010_376_a3

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[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