Sobolev orthogonal polynomials defined via gradient on the unit ball

Authors:
Yuan Xu
Affiliations:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222, USA
Venue:
Journal of Approximation Theory
Year:
2008

Citing 4
Cited 2

On polynomials orthogonal with respect to certain Sobolev inner products

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Analytic aspects of Sobolev orthogonal polynomials revisited

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Optimizing Schrödinger Functionals Using Sobolev Gradients: Applications to Quantum Mechanics and Nonlinear Optics

SIAM Journal on Scientific Computing
A family of Sobolev orthogonal polynomials on the unit ball

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New steps on Sobolev orthogonality in two variables

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Full length article: Weighted Sobolev orthogonal polynomials on the unit ball

Journal of Approximation Theory

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Abstract

An explicit family of polynomials on the unit ball B^d of R^d is constructed, so that it is an orthonormal family with respect to the inner product=@r@!"B"^"d@?f(x).@?g(x)dx+L(fg),where @r0, @? is the gradient, and L(fg) is either the inner product on the sphere S^d^-^1 or f(0)g(0).