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Integrable-square solutions of a singular ordinary differential equation

Published online by Cambridge University Press:  14 November 2011

Richard C. Gilbert
Richard C. Gilbert
Affiliation:
Mathematics Department, California State University, Fullerton, California, U.S.A.
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Synopsis

Absolutely square integrable solutions are determined for the equation = λ y where the ζn−r(x) are holomorphic in a sector of the complex plane and have asymptotic expansions as x approaches infinity. It is shown that the number of such solutions depends upon the roots of the characteristic equation and their multiplicity, and upon the sign of the derivative of the characteristic polynomial. Application is made to formally symmetric ordinary differential operators.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 89 , Issue 3-4 , 1981 , pp. 267 - 279
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

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