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Symmetric multiparameter problems and deficiency index theory

Published online by Cambridge University Press:  13 July 2011

Patrick J. Browne  and
Hamlet Isaev
Patrick J. Browne
Affiliation:
Department of Mathematics and StatisticsUniversity of CalgaryCalgaryAlbertaCanadaT2N 1N4
Hamlet Isaev
Affiliation:
Institute for Mathematics and MechanicsAcademy of Science of Azerbaijan S.S.R.Baku, U.S.S.R.
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In this article we study the multiparameter generalization of standard deficiency index theory. A classical result in this area states that if T is a symmetric operator in a Hilbert space then the dimension of the null space of T*−λI, λ∈ℂ, is constant for λ belonging to the upper (or lower) half-plane and further, when these two constants are equal, T admits a self-adjoint extension.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 3 , October 1988 , pp. 481 - 488
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

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