Transformation of Linear Spaces and Linear Operators by Inverse Reversion

Author: Elconin, Victor

Year: 1952

Degree: Dissertation (Ph.D.)

Advisor: Michal, Aristotle D.

Committee Member: Unknown, Unknown

Option: Mathematics; Physics

DOI: 10.7907/RV02-JW45

Abstract

This thesis develops a new method for transforming and extending the classes of operators and operands which appear in certain linear operations in such a way that restrictions on the ranges and domains of the operands and on the algebraic manipulation of the operators are reduced and removed. In particular, the method leads to a complete rationalization of the P operators and impulse 'functions' employed by Heaviside, Dirac and others in the analysis of certain linear systems.

In this method, the operators A of a primary class K are, in effect, first reversed, forming A*, then inverted, forming A*-1, the inverse reverse of A, and these operators are utilized to effect the remaining transformations and class extensions. The method is therefore epitomized by the phrase inverse reversion.

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