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Transformation of Linear Spaces and Linear Operators by Inverse Reversion


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.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics and Physics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Michal, Aristotle D.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1952
Record Number:CaltechTHESIS:10112017-134914663
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10505
Deposited By: Benjamin Perez
Deposited On:11 Oct 2017 21:36
Last Modified:10 May 2023 23:48

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