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Darboux Transformations, Green's Functions, and Spectral Shifts

Analysis, Dynamics, and Applications Seminar

Darboux Transformations, Green's Functions, and Spectral Shifts
Series: Analysis, Dynamics, and Applications Seminar
Location: MATH 402
Presenter: Dylan Murphy, School of Information, University of Arizona

Darboux transformations allow the construction of new potentials for (discrete or continuous) Sturm-Liouville operators. These transformations are of interest due to their application in constructing and studying solutions of the integrable systems which are related to the spectra of such operators. In this talk, I will review some recent results on a class of Darboux transformations known as "additions," and explore their relationship to the spectral shift function introduced by Krein to study trace-class perturbations of these operators.