Transformation of Linear Spaces and Linear Operators by Inverse Reversion

Citation

Elconin, Victor (1952) Transformation of Linear Spaces and Linear Operators by Inverse Reversion. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/RV02-JW45. https://resolver.caltech.edu/CaltechTHESIS:10112017-134914663

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.

Thesis Files