Common Zeros of Polynominals in Several Variables and Higher Dimensional Quadrature

Presents a systematic study of the common zeros of polynomials in several variables which are related to higher dimensional quadrature. The author uses a new approach which is based on the recent development of orthogonal polynomials in several variables and differs significantly from the previous ones based on algebraic ideal theory. Featuring a great deal of new work, new theorems and, in many cases, new proofs, this self-contained work will be of great interest to researchers in numerical analysis, the theory of orthogonal polynomials and related subjects.

IntroductionPreliminaries and lemmasMotivationsCommon zeros of polynomials in several variables: first caseMoller's lower bound for cubatureformulaExamplesCommon zeros of polynomials in several variables: general caseCubature formulae of even degreeFinal discussions