Explicit Krein resolvent identities for singular Sturm-Liouville operators with applications to Bessel operators

Abstract

We derive explicit Krein resolvent identities for generally singular Sturm-Liouville operators in terms of boundary condition bases and the Lagrange bracket.As an application of the resolvent identities obtained, we compute the trace of the resolvent difference of a pair of self-adjoint realizations of the Bessel expression -d 2 /dx 2 + (ν 2 -(1/4))x -2 on (0,∞) for values of the parameter ν ∈ [0,1) and use the resulting trace formula to explicitly determine the spectral shift function for the pair.

Locations

• Operators and Matrices - View - PDF
• arXiv (Cornell University) - View - PDF