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A generalisation of Niessen's limit-circle criterion

Published online by Cambridge University Press:  14 February 2012

Christer Bennewitz
Christer Bennewitz
Affiliation:
Department of Mathematics, University of Uppsala
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Synopsis

Let S and T be formally symmetric ordinary differential operators defined on a real interval I. It is assumed that the order of S is constant and everywhere strictly higher than the possibly varying order of T. The main result of this paper (Theorem 2.3) gives necessary and sufficient conditions for maximality of the deficiency indices of the differential relation Su = Tv considered in a Hilbert space with a scalar product which is a Dirichlet integral (see section 2) belonging to S. The conditions generalise those given in [5] for less general choices of operators S and T. For certain choices of Dirichlet integral they are explicit integrability conditions on the coefficients of the Dirichlet integral and the operator T.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 1-2 , 1977 , pp. 81 - 90
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

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