On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols

In this article we consider direct and inverse problems for ?-stable, elliptic nonlocal operators whose kernels are possibly only supported on cones which satisfy the structural condition of directional antilocality as introduced by Y. Ishikawa in 80s. We Dirichlet problem these respective “domain dependence operator” several, adapted function spaces. This formulation allows one to avoid natural “gauges” would else have be considered study associated problems. Exploiting complement investigation with infinite data single measurement uniqueness results Here, due antilocality, new geometric conditions arise domains. discuss both setting symmetric a particular class non-symmetric operators, contrast corresponding “one-sided operators” phenomena emerge problems: For instance, it is possible spaces involving local data, unique continuation property may not hold general further restrictions set arise.