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论文类型：期刊论文

发表时间：2004-09-01

发表刊物：Journal of Information and Computational Science

收录刊物：Scopus、EI

卷号：1

期号：1

页面范围：103-106

ISSN号：15487741

关键字：Integration; Invariance; Matrix algebra; Numerical methods, Bivariate orthogonal polynomials; Common zeros; Eigenfunction; Invariant factor; Jacobi matrix; Orthogonal polynomials of two variables; Stieltjes type theorems, Polynomials

摘要：Some new properties with respect to bivariate orthogonal polynomials are studied from an invariant factor point of view. The main result states if the zeros of the invariant factor   ky(x) are distinct, then   ky(x) is the eigenfunction of the corresponding truncated Jacobi matrix. We shall also present a detailed investigation of the location of the common zeros of bivariate orthogonal polynomials. A simple application to cubature formulae is given in the end. Most of them can be regarded as the extension of the univariate cases. The results also offer a new method for studying bivariate orthogonal polynomials.