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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 456, Pages 125–134
(Mi znsl6426)
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To the theory of the $C_0$-operator orthogonal polynomials
V. A. Kostin, M. N. Nebol'sina Voronezh State University, Voronezh, Russia
Abstract:
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.
Key words and phrases:
orthogonal polynomials, operator polynomials, strongly continuous semigroup generator, Bessel operator functions.
Received: 05.06.2017
Citation:
V. A. Kostin, M. N. Nebol'sina, “To the theory of the $C_0$-operator orthogonal polynomials”, Investigations on linear operators and function theory. Part 45, Zap. Nauchn. Sem. POMI, 456, POMI, St. Petersburg, 2017, 125–134; J. Math. Sci. (N. Y.), 234:3 (2018), 350–356
Linking options:
https://www.mathnet.ru/eng/znsl6426 https://www.mathnet.ru/eng/znsl/v456/p125
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Abstract page: | 138 | Full-text PDF : | 45 | References: | 22 |
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