A simultaneous almost everywhere central limit theorem for diffusions and its application to path energy and eigenvalues of the Laplacian
Gunnar A. Brosamler · Illinois Journal of Mathematics · 1990
{g, a > 0} were defined in [3] in terms of the fundamental solution of the heat equation.To be precise, if p is the solution of 0p 0--(t,x,r) 7Ayp(t,x,r), p(0+,x,y) Tx(y), with 3' the total Riemann measure of (M, ), for a > 0 we let (1.1) ga(x, y) F(a ta-l{ p(t' x, y) 1} dt, x, y M.