Consequences of the connection formulae for Sturm-Liouville spectral functions
2002 ◽
Vol 132
(2)
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pp. 387-393
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Keyword(s):
For a special case of the Sturm-Liouville equation, −(py′)′ + qy = λwy on [0, ∞) with the initial condition y(0) cos α + p(0)y′(0) sin α = 0, α ∈ [0, π), it is shown that, given the spectral derivative for two values of α ∈ [0, π) at a fixed μ = Re{λ} ≥ Λ0, it is possible to uniquely determine . An explicit formula is derived to accomplish this. Further, in a more general case of the Sturm-Liouville problem for μ with both finite and positive, then the following inequality holds
2000 ◽
Vol 130
(1)
◽
pp. 25-34
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2004 ◽
Vol 134
(1)
◽
pp. 215-223
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Keyword(s):
1988 ◽
Vol 108
(3-4)
◽
pp. 201-228
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1971 ◽
Vol 69
(2)
◽
pp. 139-148
1948 ◽
Vol 44
(2)
◽
pp. 242-250
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1967 ◽
Vol 63
(2)
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pp. 473-475
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Keyword(s):
1994 ◽
Vol 37
(1)
◽
pp. 57-72
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Keyword(s):