Email this article A Class of Orthogonal Polynomials on the Boundary of an Ellipse
- Authors: Nikolaev V.G.1
-
Affiliations:
- Novgorod State University
- Issue: Vol 239, No 3 (2019)
- Pages: 363-380
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242676
- DOI: https://doi.org/10.1007/s10958-019-04311-z
- ID: 242676
Cite item
Open Access
Access granted
Subscription Access
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.
About the authors
V. G. Nikolaev
Novgorod State University
Author for correspondence.
Email: vg14@inbox.ru
Russian Federation, 41, Bol’shaya St.-Peterburgskaya ul., Velikiy Novgorod, 173003
