Citation
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. https://resolver.caltech.edu/CaltechTHESIS:08312017-131704186
Abstract
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.)) |
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| 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) |
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| Thesis Committee: |
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| Defense Date: | 1 January 1952 |
| Record Number: | CaltechTHESIS:08312017-131704186 |
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:08312017-131704186 |
| DOI: | 10.7907/M50E-1N29 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 10405 |
| Collection: | CaltechTHESIS |
| Deposited By: | Benjamin Perez |
| Deposited On: | 31 Aug 2017 20:37 |
| Last Modified: | 10 May 2023 23:21 |
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