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On the Friedrichs extension of semi-bounded difference operators

Published online by Cambridge University Press:  24 October 2008

M. Benammar  and
W. D. Evans
M. Benammar
Affiliation:
Science Wing, Air College (Dafra Base), P.O. Box 45373, Abu Dhabi, United Arab Emirates
W. D. Evans
Affiliation:
School of Mathematics, University of Wales College of Cardiff, Senghennydd Road, Cardiff CF2 4AG
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Extract

In [5] Kalf obtained a characterization of the Friedrichs extension TF of a general semi-bounded Sturm–Liouville operator T, the only assumptions made on the coefficients being those necessary for T to be defined. The domain D(TF) of TF was described in terms of ‘weighted’ Dirichiet integrals involving the principal and non-principal solutions of an associated non-oscillatory Sturm–Liouville equation. Conditions which ensure that members of D(TF) have a finite Dirichlet integral were subsequently given by Rosenberger in [7].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 1 , July 1994 , pp. 167 - 177
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

REFERENCES

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