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Self-adjoint subspace extensions satisfying λ-linear boundary conditions

Published online by Cambridge University Press:  14 November 2011

Harald Röh
Harald Röh
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh
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Synopsis

Let S be a symmetric subspace in a Hilbert space ℋ2 with finite equal deficiency indices and let S* be its adjoint subspace in ℋ2. We consider those self-adjoint subspace extensions ℋ of S into some larger Hilbert spaces ℋ2 = (ℋ × ℂm)2 which satisfy H⋂({0} × ℂm)2 = {{0,0}}. These extensions H are characterized in terms of inhomogeneous boundary conditions for S*; they are associated with eigenvalue problems for S* depending on λ-linear boundary conditions, which we also characterize.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 1-2 , 1981 , pp. 107 - 124
Copyright
Copyright © Royal Society of Edinburgh 1981

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