Sobolev orthogonal polynomials on a simplex

Details Sobolev orthogonal polynomials on a simplex Sobolev orthogonal polynomials on a simplex

2011-11-13

arxiv.org/abs/1111.2994v1

Mathematics

Classical Analysis and ODEs

32 pages

Scientific paper

The Jacobi polynomials on the simplex are orthogonal polynomials with respect to the weight function $W_\bg(x) = x_1^{\g_1} ... x_d^{\g_d} (1- |x|)^{\g_{d+1}}$ when all $\g_i > -1$ and they are eigenfunctions of a second order partial differential operator $L_\bg$. The singular cases that some, or all, $\g_1,...,\g_{d+1}$ are -1 are studied in this paper. Firstly a complete basis of polynomials that are eigenfunctions of $L_\bg$ in each singular case is found. Secondly, these polynomials are shown to be orthogonal with respect to an inner product which is explicitly determined. This inner product involves derivatives of the functions, hence the name Sobolev orthogonal polynomials.

Affiliated with

Also associated with

No associations

Rating

Sobolev orthogonal polynomials on a simplex does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sobolev orthogonal polynomials on a simplex, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sobolev orthogonal polynomials on a simplex will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-340501