THE REPRESENTATION OF STRONGLY CONTINUOUS OPERATOR SEMIGROUPS ON VECTOR BUNDLES AS HIDA DISTRIBUTIONS

Abstract

Let E → M be a vector bundle over a compact manifold. In this short note we prove that the Schrödinger semigroup (complex heat semigroup) associated to a self-adjoint (non-negative self-adjoint) operator in ΓL2(M, E) corresponds to a ΓL2(M, E)*-valued Hida distribution, which depends continuously (holomorphically) on the time parameter.