Phd records
https://feeds.library.caltech.edu/people/Boehme-Thomas-Kelman/Phd.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 18:51:38 +0000Operation Calculus and the Finite Part of Divergent Integrals
https://resolver.caltech.edu/CaltechETD:etd-02222006-154540
Authors: {'items': [{'id': 'Boehme-Thomas-Kelman', 'name': {'family': 'Boehme', 'given': 'Thomas Kelman'}, 'show_email': 'NO'}]}
Year: 1960
DOI: 10.7907/P33D-3W91
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
In this thesis the operational calculus of J. Mikusinski is utilized to study the finite part of divergent convolution integrals.
In Chapters 2 and 3 the idea of an analytic operator function is utilized. An operator function f(z) is said to be an analytic operator function on an open region S of the complex plane if there is an operator [...] such that af(z) = {af(z, t)} has a partial derivative with respect to z which is continuous on [...]. Let f(z) be an analytic operator function and suppose that {f(z, t)} is a continuous function on [...]. Suppose also that for each t > 0 f(z, t) is an analytic function of z on a larger region S* > S. Let f*(z) be an analytic operator function on S* which is such that f*(z) = f(z) on S. Then the operator function f*(z) is called [FP f (z, t)] on S*.
The relationship between the operator product g[FP f(z,t)] and [...] is studied for the case when {f( z,t)} = [...], where m is function which possesses continuous derivatives of some order on [...].
In Chapter 4 the solutions to the singular integral equation [...] all t > 0 are found from considering the operators [...].
In Chapter 5 a type of generalized wave function is discussed.https://thesis.library.caltech.edu/id/eprint/710