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Operation Calculus and the Finite Part of Divergent Integrals


Boehme, Thomas Kelman (1960) Operation Calculus and the Finite Part of Divergent Integrals. Dissertation (Ph.D.), California Institute of Technology. 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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Erdélyi, Arthur
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1960
Record Number:CaltechETD:etd-02222006-154540
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:710
Deposited By: Imported from ETD-db
Deposited On:02 Mar 2006
Last Modified:07 Nov 2023 17:30

Thesis Files

PDF (Boehme_tk_1960.pdf) - Final Version
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