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Operational calculus and the finite part of divergent integrals

Citation

Boehme, Thomas Kelman (1960) Operational calculus and the finite part of divergent integrals. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-02222006-154540

Abstract

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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.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Erdelyi, Arthur
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1960
Record Number:CaltechETD:etd-02222006-154540
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-02222006-154540
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:710
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:02 Mar 2006
Last Modified:26 Dec 2012 02:31

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