Colloquium Seminar
Friday, January 17, 2020, 12:00pm, Physics 130
Wilfrid Gangbo (UCLA)
A partial Laplacian on a quotient Hilbert space and on the Wasserstein space
Abstract:- We consider the quotient of the Hilbert space
^d;\mathbb{R}^d)= \mathbb{R}^d\oplus\mathbb{H}_0$)
, by the set of measure preserving maps on ^d)
. This is nothing but the set of Borel measures of finite second moments on 
. We study a partial trace of the hessian on a subset of functions defined on the quotient space and verify a distinctive smoothing effect of the "heat flows" they generate for a particular class of initial conditions. To this end, we develop a theory of Fourier analysis and conic surfaces and identify a measure which allows for an integration by parts.
(This is a joint work with Y.T. Chow).
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