Faculty Publications

Title

Connection formulae for spectral functions associated with singular Dirac equations

Document Type

Conference

Journal/Book/Conference Title

Royal Society of Edinburgh - Proceedings A

Volume

134

Issue

1

First Page

215

Last Page

223

Abstract

We consider the Dirac equation given by y′ = ((- (λ-c+v2p-pλ+c+v1)) y, y = (y2y1) on [0, ∞), with initial condition y 1 (0) cos α + y2 (0) sin α = 0, α ∈[0, π) and suppose the equation is in the limit-point case at infinity. Using ρ′α(μ) to denote the derivative of the corresponding spectral function, a formula for ρ′β(μ) is given when ρ′αa(μ) is known and positive for three distinct values of α. In general, if ρ′α(μ) is known and positive for only two distinct values of α, then ρ′β(μ) is shown to be one of two possibilities. However, in special cases of the Dirac equation, ρ′ β(μ) can be uniquely determined given ρ′α(μ) for only two values of α.

Original Publication Date

1-1-2004

DOI of published version

10.1017/s0308210500003176

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