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Geometry of Finite Dimensional Moment Spaces and Applications to Orthogonal Polynomials


Comba, Paolo (1952) Geometry of Finite Dimensional Moment Spaces and Applications to Orthogonal Polynomials. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/M50E-1N29.


Various geometrical properties of the finite dimensional moment spaces generated by normalized distribution functions over [0,∞) and (-∞,∞) are investigated. The moment spaces are found to be dual to the polynomial spaces. The structure of the latter is studied by means of this duality and of a representation theorem for positive polynomials. The extreme points of the polynomial spaces are associated with polynomials orthogonal with respect to the distributions generating the moment spaces. This correspondence is used in order to derive several properties of orthogonal polynomials.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics and Aeronautics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Minor Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bohnenblust, Henri Frederic
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1952
Record Number:CaltechTHESIS:08312017-131704186
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10405
Deposited By: Benjamin Perez
Deposited On:31 Aug 2017 20:37
Last Modified:10 May 2023 23:21

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