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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| Format: | Others |
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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> |
| Summary: | 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. |
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