This thesis develops a new method for transformingand extending the classes of operators and operands which appear incertain linear operations in such a way that restrictions on theranges and domains of the operands and on the algebraic manipulationof the operators are reduced and removed. In particular, themethod leads to a complete rationalization of the P operators andimpulse 'functions' employed by Heaviside, Dirac and others in theanalysis of certain linear systems.
In this method, the operators A of a primary class Kare, in effect, first reversed, forming A*, then inverted, forming A*-1, the inverse reverse of A, and these operators areutilized to effect the remaining transformations and classextensions. The method is therefore epitomized by the phraseinverse reversion.
