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An abstract multiparameter spectral theory
Published online by Cambridge University Press: 14 November 2011
Synopsis
We consider the eigenvalue problem
for self-adjoint operators Ai and Bij on separable Hilbert spaces Hi. It is assumed that and Bij are bounded with compact. Various properties of the eigentuples λi, and xi are deduced under a “definiteness condition” weaker than those used by previous authors, at least in infinite dimensions. In particular, a Parseval relation and eigenvector expansion are derived in a suitably constructed tensor product space.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 3-4 , 1982 , pp. 193 - 204
- Copyright
- Copyright © Royal Society of Edinburgh 1982
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