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Commuting linear differential expressions

Published online by Cambridge University Press:  14 November 2011

M. Giertz ,
M. K. Kwong  and
A. Zettl
M. Giertz
Affiliation:
Department of Mathematics, The Royal Institute of Technology, 10040 Stockholm 70, Sweden
M. K. Kwong
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, U.S.A.
A. Zettl
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, U.S.A.
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Synopsis

We consider the question: When do two ordinary linear differential expressions commute? It turns out that the set of all expressions which commute with a given one form a commutative ring. Here we study the algebraic structure of these rings. As an application a complete characterization of normal differential expressions is obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 3-4 , 1981 , pp. 331 - 347
Copyright
Copyright © Royal Society of Edinburgh 1981

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