Sobolev orthogonal polynomials on product domains

2014/06/03 by Lidia Fernández, Fernández, L., Francisco Marcellán +7
Mathematics · #33C50 #42C10 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1406.0762

openalex publication_date 2014/06/03 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Orthogonal polynomials on the product domain [a₁,b₁] × [a₂,b₂] with respect to the inner product ⟨ f,g ⟩_S = ∫_a1^b₁ ∫_a2^b₂ ∇ f(x,y)⋅ ∇ g(x,y) w₁(x)w₂(y) dx dy + λf(c₁,c₂)g(c₁,c₂) are constructed, where w_i is a weight function on [a_i,b_i] for i = 1, 2, λ> 0, and (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.

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