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Analysis Seminar

Monday, November 7, 2022
3:00pm to 4:00pm
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Linde Hall 187
Complex analytic approach to spectral problems for differential operators
Ashley Ran Zhang, Department of Mathematics, University of Wisconsin, Madison,

This talk will mainly be about applications of complex function theory to inverse spectral problems for canonical systems, which constitute a broad class of second order differential equations. I will start with the basics of Krein-de Branges theory, then present an algorithm for inverse spectral problems developed by Makarov and Poltoratski for locally-finite periodic spectral measures. I will then extend the algorithm to certain classes of non-periodic spectral measures and present several examples. I will also talk about the connection between inverse spectral problems and nonlinear Fourier transform. In particular, how our examples and results for inverse spectral problems can be translated to results for nonlinear Fourier transform. This is joint work with Alexei Poltoratski.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].