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 |
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description | 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. |
doi_str_mv | 10.1007/s10958-019-04311-z |
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subjects | Complex variables Functional equations Mathematics Mathematics and Statistics Polynomials |
title | A Class of Orthogonal Polynomials on the Boundary of an Ellipse |
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