Event Type:

Department Colloquium

Date/Time:

Wednesday, July 7, 2004 - 05:00

Guest Speaker:

Richard Gundy

Institution:

Rutgers University

Abstract:

A harmonic function, composed with several dimensional Brownian Motion, produces a local martingale. Consider such a function in R^(n+1)_+, the upper-plane whose lower boundary is R^n. In order to study the boundary behavior of the function, we would like to have a version of Brownian Motion with paths fluctuating in the upper half plane, eventually arriving at the lower boundary, with translation invariant (Lebegue) hitting measure.(Think a photon coming to earth from the big bang.) Such a process exists, and can be used to give an interpretation to translation invariant singular integral operators on R^n. The Calderon reproducing formula makes an appearance in this discussion.