To the Theory of C 0-Operator Orthogonal Polynomials
Operator orthogonal polynomials are considered whose arguments are generators of strongly continuous semigroups of transformations of class C0 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 t...
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| Veröffentlicht in: | Journal of mathematical sciences (New York, N.Y.) Jg. 234; H. 3; S. 350 - 356 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Springer Nature B.V
01.10.2018
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| ISSN: | 1072-3374, 1573-8795 |
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| Abstract | Operator orthogonal polynomials are considered whose arguments are generators of strongly continuous semigroups of transformations of class C0 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 paper, more general classes of operator orthogonal polynomials are considered, which include the Jacobi and Aptekarev polynomials. Integral representations of operator fractional-rational functions and also of Bessel operator-valued functions of an imaginary argument are presented. |
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| AbstractList | Operator orthogonal polynomials are considered whose arguments are generators of strongly continuous semigroups of transformations of class C0 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 paper, more general classes of operator orthogonal polynomials are considered, which include the Jacobi and Aptekarev polynomials. Integral representations of operator fractional-rational functions and also of Bessel operator-valued functions of an imaginary argument are presented. |
| Author | Kostin, V A M. N. Nebol’sina |
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| Copyright | Copyright Springer Science & Business Media 2018 |
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| DOI | 10.1007/s10958-018-4011-x |
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| SubjectTerms | Banach spaces Chebyshev approximation Mathematical analysis Operators (mathematics) Polynomials Rational functions |
| Title | To the Theory of C 0-Operator Orthogonal Polynomials |
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