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SIGMA 14 (2018), 024, 11 pages arXiv:1704.01597
https://doi.org/10.3842/SIGMA.2018.024
Contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14)
Fourier Series of Gegenbauer-Sobolev Polynomials
Óscar Ciaurri and Judit Mínguez
Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006 Logroño, Spain
Received January 19, 2018, in final form March 13, 2018; Published online March 17, 2018
Abstract
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.
Key words:
Sobolev-type inner product; Sobolev polynomials; Gegenbauer polynomials; partial sum operator.
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