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:etd02222006154540
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): 

Thesis Committee: 

Defense Date:  1 January 1960 
Record Number:  CaltechETD:etd02222006154540 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd02222006154540 
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 ETDdb 
Deposited On:  02 Mar 2006 
Last Modified:  26 Dec 2012 02:31 
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