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Speaker: Christian Cooper, Program in Applied Mathematics
Title: An Introduction to Integro-differential Operators and their Integro-differential Equations
Abstract: By making use of standard results of harmonic analysis, in particular the application of Plancherel’s theorem and the formula for the fourier transform of a derivative, it is possible to intuitively expand the Sobolev space to allow nonintegral values. A natural place to study a rich field of operators that in essence differentiate functions with less regularity than is traditionally required. The most principle example: the fractional Laplacian, is studied and used to create a final connection between more general integro-differential operators (and their integro-differential equations) and the equivalent formation of these IDEs in divergence and non-divergence form.