Sobolev orthogonal polynomials on product domains

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:284

Article

Fernandez, Lidia¹  Marcellan, Francisco^2,3  Perez, Teresa E.¹  Pinar, Miguel A.¹  Xu, Yuan⁴ 

[1] Univ Granada, Dept Matemat Aplicada, E-18071 Granada, Spain

[2] Inst Ciencias Matemat ICMAT, Madrid, Spain

[3] Univ Carlos III Madrid, Dept Matemat, E-28903 Getafe, Spain

[4] Univ Oregon, Dept Math, Eugene, OR 97403 USA

关键词: Classical orthogonal polynomials;    Orthogonal polynomials in two variables;    Sobolev inner products;    Product domain;   

DOI  :  10.1016/j.cam.2014.09.015

来源: Elsevier

【 摘 要 】

Orthogonal polynomials on the product domain [a(1), b(1)] x [a(2), b(2)] with respect to the inner product < f, g >(s) = integral(b1)(a1) integral(b2)(a2) del f(x, y) center dot del g(x, y) w(1)(x)w(2)(y) dx dy +lambda f(c(1), c(2))g(c(1), c(2)) are constructed, where w(i) is a weight function on [a(i), b(i)] for i = 1, 2, lambda > 0, and (c(1), c(2)) is a fixed point. The main result shows how an orthogonal basis for such an inner product can be constructed for certain weight functions, in particular, for product Laguerre and product Gegenbauer weight functions, which serve as primary examples. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free