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VI.—On Solvability of Some Two-Parameter Eigenvalue Problems in Hilbert Space
Published online by Cambridge University Press: 14 February 2012
Synopsis
This paper studies two particular cases of the general 2-parameter eigenvalue problem namely
where A, B, B1, B2, C, C1, C2 are self-adjoint operators in Hilbert space, all except A being bounded. The disposable parameters λ and μ have to be determined so that the equations have non-trivial solutions x, y.
On the assumption that the solution is known for ∊ = o, solutions are constructed in the form of series for λ, μ, x, y as power series in ∊ with finite radius of convergence.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 68 , Issue 1 , 1968 , pp. 83 - 93
- Copyright
- Copyright © Royal Society of Edinburgh 1968
References
References to Literature
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