ar X iv : m at h / 02 06 28 1 v 1 [ m at h . A P ] 2 6 Ju n 20 02 Large time behavior of the heat kernel
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چکیده
In this paper we study the large time behavior of the (minimal) heat kernel k M P (x, y, t) of a general time independent parabolic operator L = u t +P (x, ∂ x) which is defined on a noncompact manifold M. More precisely, we prove that lim t→∞ e λ0t k M P (x, y, t) always exists. Here λ 0 is the generalized principal eigenvalue of the operator P in M .
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تاریخ انتشار 2002