VI.—On Solvability of Some Two-Parameter Eigenvalue Problems in Hilbert Space
1968 ◽
Vol 68
(1)
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pp. 83-93
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SynopsisThis paper studies two particular cases of the general 2-parameter eigenvalue problem namelywhere 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.
1984 ◽
Vol 96
(3-4)
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pp. 261-274
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1951 ◽
Vol 47
(3)
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pp. 477-482
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1981 ◽
Vol 33
(1)
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pp. 210-228
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1981 ◽
Vol 91
(1-2)
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pp. 15-30
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2003 ◽
Vol 46
(3)
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pp. 561-573
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1984 ◽
Vol 96
(1-2)
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pp. 69-78
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1987 ◽
Vol 106
(1-2)
◽
pp. 39-51
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1970 ◽
Vol 22
(1)
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pp. 134-150
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1972 ◽
Vol 18
(1)
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pp. 13-17
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