On second-order almost-periodic elliptic operators

The paper considers second-order, strongly elliptic, operators H with compl ex almost-periodic coefficients in divergence form on R-d. First, it is pro ved that the corresponding heat kernel is Holder continuous and Gaussian bo unds are derived with the correct small and large time asymptotic behaviour on the kernel and its Holder derivatives. Secondly, it is established that the kernel has a variety of properties of almost-periodicity. Thirdly, it is demonstrated that the kernel of the homogenization (H) over cap of H is the leading term in the asymptotic expansion of t \ --> K-t.