We use the Feynman-Kac formula and a decomposition of the Brownian bridge to obtain pointwise estimates on the diagonal elements of the heat kernel. We also compute bounds on trace (et?D) where ?D is the Dirichlet Laplacian for (i) a bounded region D in Rn with smooth boundary or (ii) an unbounded region D in R2 with finite area. © 1987.
|Number of pages||15|
|Journal||Journal of Functional Analysis|
|Publication status||Published - Apr 1987|