On orthogonal polynomials of Sobolev type: algebraic properties and zeros
SIAM Journal on Mathematical Analysis
Relative asymptotics for orthogonal polynomials with a Sobolev inner product
Journal of Approximation Theory
On recurrence relations for Sobolev orthogonal polynomials
SIAM Journal on Mathematical Analysis
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Krall-type orthogonal polynomials in several variables
Journal of Computational and Applied Mathematics
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Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding the evaluation of derivatives at several points to a measure, are studied. Orthogonal polynomials and kernel functions associated with this new inner product can be explicitly expressed in terms of those corresponding to the original measure. We apply our results to the Sobolev-type modification of the multivariate classical measure on the unit disk obtained by adding the outward normal derivatives on a finite set of points on the unit sphere. Then, asymptotics of Christoffel functions are studied.