Consequences of the Connection Formulae for Sturm-Liouville Spectral Functions

Suzanne Riehl University of Northern Iowa

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 ρ′_{α}(μ) for two values of α ∈ [0, π) at a fixed μ = Re{λ} ≥ Λ_{0}, it is possible to uniquely determine ρ′_{β}(μ), β ∈ [0, π). An explicit formula is derived to accomplish this.