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

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    Author
    Rung, Donald; Allan, S. Blake; Kim, Justin Hambin; Michajlyszyn, Gregory; Nichols, Roger
    Date
    2020
    Type
    Presentation
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    URI
    https://dspace.sewanee.edu/handle/11005/21680
    Subject
    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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