Título: Best polynomial approximation on the unit ball
Conferenciante: Miguel A. Piñar (Universidad de Granada)
Resumen: The purpose of this talk is to show some basic properties of the best approximation by polynomials of degree at most n on the unit ball of dimension d. In particular, we determine the connection between the error of best approximation of a function in a Sobolev space and the error of best approximation of the corresponding
derivatives. The case d=1 is classical, the extension of this result to higher dimensions, even in the ball case, contains some subtle difficulties. In fact, to obtain our estimates we need the concourse of standard and angular derivatives.
The proof of these results are based on the Fourier expansions in orthogonal polynomials with respect to the Gegenbauer weight functions on the unit ball. The key ingredients are the commuting relations between partial derivatives and the orthogonal projection operators, and explicit formulas for an explicit basis of orthogonal polynomials and their derivatives.
The relations between the orthogonal polynomials and their derivatives depend on corresponding relations for an explicit basis of spherical harmonics, which are of independent interest.
6 de octubre de 2016, 12:00, Seminario 1ª planta IEMath-GR
Más información sobre el Seminario del Grupo de Investigación FQM-384 GOYA - Grupo en Ortogonalidad y Aplicaciones aquí.