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The number of integrable-square solutions of products of differential expressions*

Published online by Cambridge University Press:  14 February 2012

W. N. Everitt  and
A. Zettl
W. N. Everitt
Affiliation:
Department of Mathematics, University of Dundee
A. Zettl
Affiliation:
Northern Illinois University, De Kalb, Illinois, USA
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Synopsis

Given differential expressions τ1; τ2, …, τn— not necessarily symmetric—which are regular on [0,∞), we investigate the relationship between the number of linearly independent L2(0,∞) solutions of the equations τjy = 0 and of the product equation (τ1τ2 … τn)y = 0. Our results extend those recently obtained in [15, 16, 17] for the special case τJ = τ for j = 1, …, n and τ is symmetric. In particular they include the classification results of Everitt and Giertz [4,5,6] for this special case when τ is a real second-order symmetric expression.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 3 , 1977 , pp. 215 - 226
Copyright
Copyright © Royal Society of Edinburgh 1977

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