A higher order Sobolev-type inner product for orthogonal polynomials in several variables

被引：0
|
作者：
Herbert Dueñas
Luis E. Garza
Miguel Piñar
机构：
[1] Universidad Nacional de Colombia,Departamento de Matemáticas
[2] Universidad de Colima,Facultad de Ciencias
[3] Universidad de Granada,Departamento de Matemática Aplicada, Facultad de Ciencias
来源：
Numerical Algorithms | 2015年 / 68卷
关键词：
Multivariate orthogonal polynomials; Asymptotics; Sobolev inner products; 33C47; 42C05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider polynomials in several variables orthogonal with respect to a Sobolev-type inner product, obtained from adding a higher order gradient evaluated in a fixed point to a standard inner product. An expression for these polynomials in terms of the orthogonal family associated with the standard inner product is obtained. A particular case using polynomials in the unit ball is analyzed, and some asymptotic results are derived.
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页码：35 / 46
页数：11
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