A Class of Orthogonal Polynomials on the Boundary of an Ellipse

A Class of Orthogonal Polynomials on the Boundary of an Ellipse

We construct a class of polynomials of one complex variable that are pairwise orthogonal with some weight on the boundary of an ellipse. We prove that an arbitrary λ-holomorphic Hölder function defined in an ellipse is represented as a series with respect to given polynomials. This result is applied...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2019-06, Vol.239 (3), p.363-380
1. Verfasser: Nikolaev, V. G.
Format: Artikel
Sprache:eng
Schlagworte:
Complex variables
Functional equations
Mathematics
Mathematics and Statistics
Polynomials
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Zusammenfassung:We construct a class of polynomials of one complex variable that are pairwise orthogonal with some weight on the boundary of an ellipse. We prove that an arbitrary λ-holomorphic Hölder function defined in an ellipse is represented as a series with respect to given polynomials. This result is applied to prove the existence and uniqueness of a solution to some functional equation in the ellipse in the Hölder classes.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04311-z