We prove by Bernstein inequality that Gauss-Jacobi(-Lobatto) nodes of suitable order are L^inf norming meshes for algebraic polynomials, in a wide range of Jacobi parameters. A similar result holds for trigonometric polynomials on subintervals of the period, by a nonlinear transformation of such nodes and Videnskii inequality.
Jacobi norming meshes
PIAZZON, FEDERICO;VIANELLO, MARCO
2016
Abstract
We prove by Bernstein inequality that Gauss-Jacobi(-Lobatto) nodes of suitable order are L^inf norming meshes for algebraic polynomials, in a wide range of Jacobi parameters. A similar result holds for trigonometric polynomials on subintervals of the period, by a nonlinear transformation of such nodes and Videnskii inequality.
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