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

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Authors
Rung, Donald
Allan, S. Blake
Kim, Justin Hambin
Michajlyszyn, Gregory
Nichols, Roger
Issue Date
2020
Type
Presentation
Keywords
Scholarship Sewanee 2020 , Operator theory , Resolvent differences , Sturm-Liouville , Bessel
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 −d2/dx2+(ν2−(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.
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