Density of Products of Solutions and the Linearized Calderón Problem in an Analytic Background

We study the linearization, with respect to zeroth-order perturbations, of the local Dirichlet-to-Neumann map of a formally self-adjoint elliptic operator $P=-Δ_g+Q$ on a compact Riemannian manifold $(M,g)$ of dimension $n\geq 2$ with boundary, where $Q$ is of order at most one. Near a boundary poin