Sobolev orthogonal polynomials on the unit ball via outward normal derivatives
| Autor: | Lidia Fernández, Miguel A. Piñar, Doron S. Lubinsky, Teresa E. Pérez, Antonia M. Delgado |
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| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Unit sphere
Christoffel symbols Pure mathematics Applied Mathematics 010102 general mathematics Spherical harmonics 010103 numerical & computational mathematics 01 natural sciences Sobolev space Mathematics - Classical Analysis and ODEs Orthogonal polynomials Classical Analysis and ODEs (math.CA) FOS: Mathematics 33C50 42C10 Ball (mathematics) 0101 mathematics Algebraic number Analysis Mathematics |
| Popis: | We analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which involves the outward normal derivatives on the sphere. Using their representation in terms of spherical harmonics, algebraic and analytic properties will be deduced. First, we deduce explicit connection formulas relating classical multivariate ball polynomials and our family of Sobolev orthogonal polynomials. Then explicit representations for the norms and the kernels will be obtained. Finally, the asymptotic behaviour of the corresponding Christoffel functions is studied. 26 pages |
| Databáze: | OpenAIRE |
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