Doob's ω-Transform on Local Dirichlet Spaces. (23rd August 2021) - Bezzarga, Mounir; Kenzizi, Tarek
Abstract: In this article, we study the existence and uniqueness of nonnegative solutions for the following parabolic problem H t ω u + ∂ u ∂ t = 0, in X × ( 0, T ), u ( x, 0 ) = u 0 ( x ), in X, where T > 0, X is a locally compact separable metric space, Ht is a operator (not necessarily selfadjoint) associated with a regular (not necessarily symmetric)local Dirichlet form E t, the initial value u 0 ∈ L 2 ( X, ω 2 d m ) and m is a positive Radon measure on Borel subset U of X such that m ( U ) > 0. Our technical approach for uniqueness is based on Täcklind type uniqueness theorem.,