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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… Click to show full abstract
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.
Keywords:
ellipse;
class orthogonal;
orthogonal polynomials;
boundary ellipse;
polynomials boundary
Journal Title: Journal of Mathematical Sciences
Year Published: 2019
Link to full text (if available)
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Journal Title: Journal of Mathematical Sciences
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!