Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 024, 11 pages      arXiv:1704.01597
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

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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