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1.—An Algorithm for the Construction of Limit Circle Expressions*†

Published online by Cambridge University Press:  14 February 2012

Anton Zettl
Anton Zettl
Affiliation:
Department of Mathematics, University of Dundee and Northern Illinois University, De Kalb.
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Synopsis

Consider the differential expression

It is shown here that given pn > 0 with pn ∈ C2n(0, ∞) there exist coefficients

such that all solutions of the equation Ry = 0 are in L2(0,∞). The pi for i<n can be explicitly obtained in terms of pn and a parameter function.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 75 , Issue 1 , 1976 , pp. 1 - 3
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

1Neumark, M. A.. Linear Differentialoperatoren (Berlin: Akademie-Verlag, 1960).CrossRefGoogle Scholar
2Walker, P. W.. Asymptotics for a class of fourth order differential expressions. J. Differential Equations 11 (1972), 321–334.CrossRefGoogle Scholar
3Zettl, A.. The limit point and limit circle cases for polynomials in a differential operator. Proc. Roy. Soc. Edinburgh Sect. A 73 (1975), 301–306.CrossRefGoogle Scholar