Connection formulae for spectral functions associated with singular Sturm–Liouville equations
Published online by Cambridge University Press: 11 July 2007
Abstract
We consider the Sturm–Liouville equation with the initial condition and suppose that Weyl's limit-point case holds at infinity. Let ρα(μ) be the corresponding spectral function and its symmetric derivative. We show that for almost all μ ∈ R, if exists and is positive for some α ∈ [0, π), then (i) exists and is positive for all β ∈ [0, π), and (ii) for all α1, α2 ∈ (0, π) \ {½ π},
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 1 , February 2000 , pp. 25 - 34
- Copyright
- Copyright © Royal Society of Edinburgh 2000
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