Generalized translation operators
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...
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1954
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| Online Access: | https://thesis.library.caltech.edu/184/1/McGregor_jl_1954.pdf McGregor, James L. (1954) Generalized translation operators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/799Z-1X12. https://resolver.caltech.edu/CaltechETD:etd-01152004-101808 <https://resolver.caltech.edu/CaltechETD:etd-01152004-101808> |
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ndltd-CALTECH-oai-thesis.library.caltech.edu-184 |
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ndltd-CALTECH-oai-thesis.library.caltech.edu-1842019-12-22T03:05:36Z Generalized translation operators McGregor, James L. 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. 1954 Thesis NonPeerReviewed application/pdf https://thesis.library.caltech.edu/184/1/McGregor_jl_1954.pdf https://resolver.caltech.edu/CaltechETD:etd-01152004-101808 McGregor, James L. (1954) Generalized translation operators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/799Z-1X12. https://resolver.caltech.edu/CaltechETD:etd-01152004-101808 <https://resolver.caltech.edu/CaltechETD:etd-01152004-101808> https://thesis.library.caltech.edu/184/ |
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Others
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NDLTD |
| description |
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. |
| author |
McGregor, James L. |
| spellingShingle |
McGregor, James L. Generalized translation operators |
| author_facet |
McGregor, James L. |
| author_sort |
McGregor, James L. |
| title |
Generalized translation operators |
| title_short |
Generalized translation operators |
| title_full |
Generalized translation operators |
| title_fullStr |
Generalized translation operators |
| title_full_unstemmed |
Generalized translation operators |
| title_sort |
generalized translation operators |
| publishDate |
1954 |
| url |
https://thesis.library.caltech.edu/184/1/McGregor_jl_1954.pdf McGregor, James L. (1954) Generalized translation operators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/799Z-1X12. https://resolver.caltech.edu/CaltechETD:etd-01152004-101808 <https://resolver.caltech.edu/CaltechETD:etd-01152004-101808> |
| work_keys_str_mv |
AT mcgregorjamesl generalizedtranslationoperators |
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1719304280063606784 |