Geometry of Finite Dimensional Moment Spaces and Applications to Orthogonal Polynomials

[摘要] Various geometrical properties of the finite dimensionalmoment spaces generated by normalized distribution functionsover [0,∞) and (-∞,∞) are investigated. The moment spacesare found to be dual to the polynomial spaces. The structureof the latter is studied by means of this duality and of arepresentation theorem for positive polynomials. The extremepoints of the polynomial spaces are associated with polynomialsorthogonal with respect to the distributions generatingthe moment spaces. This correspondence is used in order toderive several properties of orthogonal polynomials.

[发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy

[关键词] Mathematics