Integration of polyharmonic functions
The results in this paper are motivated by two analogies. First, m-harmonic functions in R(n) are extensions of the univariate algebraic polynomials of odd degree 2m-1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1996 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/37891 |
| Acceso en línea: | http://dx.doi.org/10.1090/S0025-5718-96-00747-8 http://hdl.handle.net/11449/37891 |
| Access Level: | acceso abierto |
| Palabra clave: | polyharmonic function extended cubature formula polyharmonic order of precision polyharmonic monospline |
| Sumario: | The results in this paper are motivated by two analogies. First, m-harmonic functions in R(n) are extensions of the univariate algebraic polynomials of odd degree 2m-1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes. |
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