Geodesic
To the theory of the $C_0$-operator orthogonal polynomials
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 125-134 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Operator orthogonal polynomials are considered whose argument is the generator of a strongly continuous semigroup of transformations of class $C_0$ acting in a Banach space. Earlier such polynomials were considered by the authors in the case of the Chebyshev polynomials of the first and second kind. In this article more general classes of operator orthogonal polynomials are considered, which include the Jacobi and Aptekarev polynomials. Integral representation of operator fractional-rational functions and also Bessel operator functions of imaginary argument are presented. 
@article{ZNSL_2017_456_a9,
     author = {V. A. Kostin and M. N. Nebol'sina},
     title = {To the theory of the $C_0$-operator orthogonal polynomials},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {125--134},
     year = {2017},
     volume = {456},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a9/}
}
TY  - JOUR
AU  - V. A. Kostin
AU  - M. N. Nebol'sina
TI  - To the theory of the $C_0$-operator orthogonal polynomials
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 125
EP  - 134
VL  - 456
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a9/
LA  - ru
ID  - ZNSL_2017_456_a9
ER  - 
%0 Journal Article
%A V. A. Kostin
%A M. N. Nebol'sina
%T To the theory of the $C_0$-operator orthogonal polynomials
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 125-134
%V 456
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a9/
%G ru
%F ZNSL_2017_456_a9
V. A. Kostin; M. N. Nebol'sina. To the theory of the $C_0$-operator orthogonal polynomials. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 125-134. http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a9/

[1] A. I. Aptekarev, “Asimptotika ortogonalnykh mnogochlenov v okrestnosti kontsov intervala ortogonalnosti”, Mat. sbornik, 183:5 (1992), 43–62 | MR | Zbl

[2] K. Iosida, Funktsionalnyi analiz, Mir, M., 1967 | MR

[3] V. A. Kostin, “O ravnomerno korrektnoi razreshimosti kraevykh zadach dlya abstraktnykh uravnenii s operatorom Keldysha-Fellera”, Differentsialnye uravneniya, 31:8 (1995), 1419–1425 | MR | Zbl

[4] V. A. Kostin, M. N. Nebolsina, “$C_0$-operatornye ortogonalnye mnogochleny Chebysheva i ikh predstavleniya”, Zap. nauchn. semin. POMI, 376, 2010, 64–87

[5] M. A. Krasnoselskii, P. P. Zabreiko, E. I. Pustylnik, P. E. Sobolevskii, Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966 | MR

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

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

[8] V. P. Maslov, Operatornye metody, Nauka, M., 1973 | MR

[9] M. N. Nebolsina, “Ortogonalnye mnogochleny Chebysheva i kraevaya zadacha Neimana”, Differentsialnye uravneniya, 46:3 (2010), 449–450 | MR | Zbl

[10] G. Segë, Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

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