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On the minimization of singular quadratic functional

Published online by Cambridge University Press:  14 November 2011

John S. Bradley ,
Don B. Hinton  and
Robert M. Kauffman
John S. Bradley
Affiliation:
Mathematics Department, University of Tennessee, Knoxville, Tennessee 37916, U.S.A.
Don B. Hinton
Affiliation:
Mathematics Department, University of Tennessee, Knoxville, Tennessee 37916, U.S.A.
Robert M. Kauffman
Affiliation:
Mathematics Department, University of Tennessee, Knoxville, Tennessee 37916, U.S.A.
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Synopsis

A quadratic functional Q is considered which is defined by an integral on a subset of functions in a weighted Hilbert space. The functional Q is minimized subject to the Dirichlet index of the associated differential operator being minimal. The infimum of Q is shown to be the least point in the spectrum of a certain self-adjoint operator which arises as a Friedrichs extension.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 3-4 , 1981 , pp. 193 - 208
Copyright
Copyright © Royal Society of Edinburgh 1981

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