CaltechTHESIS
A Caltech Library Service

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

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.)) California Institute of Technology Physics, Mathematics and Astronomy Mathematics Public (worldwide access) Erdelyi, Arthur Unknown, Unknown 1 January 1960 CaltechETD:etd-02222006-154540 http://resolver.caltech.edu/CaltechETD:etd-02222006-154540 No commercial reproduction, distribution, display or performance rights in this work are provided. 710 CaltechTHESIS Imported from ETD-db 02 Mar 2006 26 Dec 2012 02:31

Thesis Files

 Preview
PDF (Boehme_tk_1960.pdf) - Final Version
See Usage Policy.

2057Kb

Repository Staff Only: item control page