Fourier Series of Gegenbauer-Sobolev Polynomials

[摘要] 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.

[关键词] Sobolev-type inner product;Sobolev polynomials;Gegenbauer polynomials;partial sum operator