On the Explicit Representation of Polyorthogonal Polynomials

In the work, new concepts are introduced: an admissible index, an almost perfect system of functions. Using these concepts for an arbitrary system of power series of Laurent type, a criterion for the uniqueness of a polyorthogonal polynomial associated with this system is formulated and proved. The...

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Bibliographic Details
Published in:Russian mathematics 2021-04, Vol.65 (4), p.72-80
Main Author: Starovoitov, A. P.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:In the work, new concepts are introduced: an admissible index, an almost perfect system of functions. Using these concepts for an arbitrary system of power series of Laurent type, a criterion for the uniqueness of a polyorthogonal polynomial associated with this system is formulated and proved. The explicit form of this polynomial is found, as well as the explicit form of polynomials in the numerator and denominator of the corresponding Padé approximations. The proved assertions complement the well-known results in the theory of polyorthogonal polynomials and Padé approximations.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X2104006X