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Generalized Translation Operators


McGregor, James Lewin (1954) Generalized Translation Operators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/799Z-1X12.


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.))
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 1954
Record Number:CaltechETD:etd-01152004-101808
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:184
Deposited By: Imported from ETD-db
Deposited On:16 Jan 2004
Last Modified:13 Jun 2023 20:53

Thesis Files

PDF (McGregor_jl_1954.pdf) - Final Version
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