Berstein-type quasi-interpolants
Curves and surfaces
Bernstein-Durrmeyer polynomials on a simplex
Journal of Approximation Theory
A note on Bernstein-Durrmeyer operators in L2(S)
Journal of Approximation Theory
Strong converse inequality for the Bernstein-Durrmeyer operator
Journal of Approximation Theory
Approximation on simplices with respect to weighted Sobolev norms
Journal of Approximation Theory
An identity for multivariate Bernstein polynomials
Computer Aided Geometric Design
An identity for a general class of approximation operators
Journal of Approximation Theory
Studying Baskakov--Durrmeyer operators and quasi-interpolants via special functions
Journal of Approximation Theory
Complete asymptotic expansion for multivariate Bernstein-Durrmeyer operators and quasi-interpolants
Journal of Approximation Theory
Multivariate Bernstein-Durrmeyer operators with arbitrary weight functions
Journal of Approximation Theory
Hi-index | 0.00 |
A new class of differential operators on the simplex is introduced, which define weighted Sobolev norms and whose eigenfunctions are orthogonal polynomials with respect to Jacobi weights. These operators appear naturally in the study of quasi-interpolants which are intermediate between Bernstein-Durrmeyer operators and orthogonal projections on polynomial subspaces. The quasi-interpolants satisfy a Voronovskaja-type identity and a Jackson-Favard-type error estimate. These and further properties follow from a spectral analysis of the differential operators. The results are based on a pointwise orthogonality relation of Bernstein polynomials that was recently discovered by the authors.