Dawid Hanrahan

Emulating the Darcy Solution Operator by Heat-Semigroup Functional Calculus and Pointwise Products

We approximate the solution operator $(a,f)\mapsto u$ of $-\operatorname{div}(a\nabla u)=f$ by operator networks whose only primitives are heat-semigroup functions of a fixed reference operator and pointwise products. The main result is an emulation theorem on strongly local Dirichlet spaces with a spectral gap and a B...