Citation
McGregor, James Lewin (1954) Generalized Translation Operators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/799Z-1X12. https://resolver.caltech.edu/CaltechETD:etd-01152004-101808
Abstract
A study is made of generalized translation operators of the Delsarte-Levitan-Povzner type. After reviewing the method of associating such operators with linear second order differential equations, an abstract theory is developed with the aim of constructing an L[subscript 1]-convolution algebra. The chief novelty is a device of comparing one family of translation operators with another "known" family. The Plancherel theorem and Bochner's theorem on positive definite functions are derived by the Krein-Godement method of locally compact group theory. An application to the classical Sturm-Liouville problem is discussed.
| 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) |
| Research Advisor(s): |
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| Thesis Committee: |
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| Defense Date: | 1 January 1954 |
| Record Number: | CaltechETD:etd-01152004-101808 |
| Persistent URL: | https://resolver.caltech.edu/CaltechETD:etd-01152004-101808 |
| DOI: | 10.7907/799Z-1X12 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 184 |
| Collection: | CaltechTHESIS |
| Deposited By: | Imported from ETD-db |
| Deposited On: | 16 Jan 2004 |
| Last Modified: | 13 Jun 2023 20:53 |
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