A partial Laplacian on a quotient Hilbert space and on the Wasserstein space

We consider the quotient of the Hilbert space...by the set of measure preserving maps on... 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). - see full abstract at event URL.