Turkish Journal of Mathematics
Abstract
Let {q_n^{(\alpha,\beta)}}_{n \geq 0} be the sequence of polynomials orthonormal with respect to the Sobolev inner product \langle f,g\rangle_S:=\int_{-1}^1f(x)g(x)w^{(\alpha,\beta)}(x)dx+\int_{-1}^1f'(x)g'(x)w^{(\alpha+1,\beta+1)}(x)dx, where w^{(\alpha,\beta)}(x)=(1-x)^{\alpha}(1+x)^{\beta}, x\in [-1,1] and \alpha,\beta>-1. This paper explores the convergence in the W^{1,p}\left((-1,1), (w^{(\alpha,\beta)},w^{(\alpha+1,\beta+1)})\right) norm of the Fourier expansion in terms of {q_n^{(\alpha,\beta)}}_{n\geq 0} with 1< p
DOI
10.3906/mat-1208-29
Keywords
Sobolev orthogonal polynomials, weighted Sobolev spaces, Fourier expansions, Sobolev--Fourier expansions
First Page
934
Last Page
948
Recommended Citation
MARCELLÁN, F, QUINTANA, Y, & URIELES, A (2013). On the Pollard decomposition method applied to some Jacobi--Sobolev expansions. Turkish Journal of Mathematics 37 (6): 934-948. https://doi.org/10.3906/mat-1208-29
