Transformation of Linear Spaces and Linear Operators by Inverse Reversion

Mathematics

Elconin, Victor ; Michal, Aristotle D.

University:California Institute of Technology

Department:Physics, Mathematics and Astronomy

关键词: Mathematics;   

Others  :  https://thesis.library.caltech.edu/10505/2/Elconin_V_1952.pdf

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来源: Caltech THESIS

【 摘 要 】

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.