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Prabhu
Posts:
11
Registered:
10/24/08


zeros of heatextensions, Brownian motion
Posted:
May 26, 2011 8:00 AM


Hi, if I take an nontrivial L^2 function f on R^n, its heat extension F in R^{n+1}_+ is real analytic on each plane and nonzero almost everywhere. (correct?)
1. How bad can its zero set be?
In particular,
2. Let Z be Brownian motion in R^n x [0,oo), started at (0, T). Can I say that the process F(Z_t) is almost surely nonzero for all t>0? (till Z hits boundary). Or is that F(Z_t) is nonzero for all t>0, almost surely?
Thanks.
Prabhu



