A result on common zeros location of orthogonal polynomials in two variables

[摘要] The aim of this paper is to investigate some general properties of common zeros of orthogonal polynomials in two variables for any given region D subset of R-2 from a view point of invariant factor. An important result is shown that if X-0 is a common zero of all the orthogonal polynomials of degree k then the intersection of any line passing through X-0 and D is not empty. This result can be used to settle the problem of location of common zeros of orthogonal polynomials in two variables. The main result of the paper can be considered as an extension of the univariate case. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] orthogonal polynomials of two variables;invariant factors;common zeros location