Fourier Series of Gegenbauer-Sobolev Polynomials

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• ISSN: 1815-0659
• Main Authors: Ciaurri, Ó., Mínguez, J.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209440
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Fourier Series of Gegenbauer-Sobolev Polynomials / Ó. Ciaurri, J. Mínguez // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 16 назв. — англ.

We study the partial sum operator for a Sobolev-type inner product related to the classical Gegenbauer polynomials. A complete characterization of the partial sum operator in an appropriate Sobolev space is given. Moreover, we analyze the convergence of the partial sum operators.