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Transformations of second order ordinary and partial difierential operators

Published online by Cambridge University Press:  14 November 2011

Calvin D. Ahlbrandt ,
Don B. Hinton  and
Roger T. Lewis
Calvin D. Ahlbrandt
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211, U.S.A.
Don B. Hinton
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37916, U.S.A.
Roger T. Lewis
Affiliation:
Department of Mathematics, University of Alabama in Birmingham, Birmingham, Alabama 35294, U.S.A.
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Synopsis

Liouville type transformations are given for symmetric linear ordinary and partial differential operators of second order. Explicit formulas are given for the coefficients of the transformed operators. As a corollary to the general theory we obtain an “Atkinson form” for certain first order vector partial differential operators. This leads to a generalization of the concept of “g-unitary” transformations. Applications to oscillation and spectral theories are included.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 1-2 , 1982 , pp. 31 - 49
Copyright
Copyright © Royal Society of Edinburgh 1982

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