Journals / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 6
On the Pollard decomposition method applied to some Jacobi--Sobolev expansions
- Pages
- 934–948
- DOI
- —
Abstract
Let {qn(a,b)}n \geq 0 be the sequence of polynomials orthonormal with respect to the Sobolev inner product \langle f,g\rangleS:=\int-11f(x)g(x)w(a,b)(x)dx+\int-11f'(x)g'(x)w(a+1,b+1)(x)dx, where w(a,b)(x)=(1-x)a(1+x)b, x\in [-1,1] and a,b>-1. This paper explores the convergence in the W1,p\left((-1,1), (w(a,b),w(a+1,b+1))\right) norm of the Fourier expansion in terms of {qn(a,b)}n\geq 0 with 1< p
Özet
Let {qn(a,b)}n \geq 0 be the sequence of polynomials orthonormal with respect to the Sobolev inner product \langle f,g\rangleS:=\int-11f(x)g(x)w(a,b)(x)dx+\int-11f'(x)g'(x)w(a+1,b+1)(x)dx, where w(a,b)(x)=(1-x)a(1+x)b, x\in [-1,1] and a,b>-1. This paper explores the convergence in the W1,p\left((-1,1), (w(a,b),w(a+1,b+1))\right) norm of the Fourier expansion in terms of {qn(a,b)}n\geq 0 with 1< p