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arXiv · 1908.05392

Explicit Krein Resolvent Identities for Singular Sturm-Liouville Operators with Applications to Bessel Operators

S. Blake Allan·Justin Hanbin Kim·Gregory Michajlyszyn·Roger Nichols·Don Rung
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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 $-d^2/dx^2+(\nu^2-(1/4))x^{-2}$ on $(0,\infty)$ for values of the parameter $\nu\in[0,1)$ and use the resulting trace formula to explicitly determine the spectral shift function for the pair.

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S. Blake Allan, Justin Hanbin Kim, Gregory Michajlyszyn, Roger Nichols, Don Rung. 2019-08-15. Explicit Krein Resolvent Identities for Singular Sturm-Liouville Operators with Applications to Bessel Operators. https://arxiv.org/abs/1908.05392

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