pith. sign in

arxiv: math/0612527 · v1 · submitted 2006-12-18 · 🧮 math.CA

Sobolev orthogonal polynomials defined via gradient on the unit ball

classification 🧮 math.CA
keywords nablaballfamilygradientinnerpolynomialsproductunit
0
0 comments X
read the original abstract

An explicit family of polynomials on the unit ball $B^d$ of $\RR^d$ is constructed, so that it is an orthonormal family with respect to the inner product $$ < f,g > = \rho \int_{B^d}\nabla f(x)\cdot \nabla g(x) dx + \CL (fg), $$ where $\rho >0$, $\nabla$ is the gradient, and $\CL(fg)$ is either the inner product on the sphere $S^{d-1}$ or $f(0)g(0)$.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.