To the Theory of C0-Operator Orthogonal Polynomials

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.