Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4638508 | Journal of Computational and Applied Mathematics | 2015 | 14 Pages |
Abstract
Orthogonal polynomials on the product domain [a1,b1]×[a2,b2][a1,b1]×[a2,b2] with respect to the inner product 〈f,g〉S=∫a1b1∫a2b2∇f(x,y)⋅∇g(x,y)w1(x)w2(y)dxdy+λf(c1,c2)g(c1,c2) are constructed, where wiwi is a weight function on [ai,bi][ai,bi] for i=1,2i=1,2, λ>0λ>0, and (c1,c2)(c1,c2) 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Lidia Fernández, Francisco Marcellán, Teresa E. Pérez, Miguel A. Piñar, Yuan Xu,