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- W3204546543 abstract "In this article we consider direct and inverse problems for $alpha$-stable, elliptic nonlocal whose kernels are possibly only supported on cones and which satisfy the structural condition of emph{directional antilocality} as introduced in cite{I86}. We consider the Dirichlet problem for these on the domain of dependence of the operator and in several, adapted function spaces. This formulation allows one to avoid natural gauges which would else have to be considered in the study of the associated inverse problems. Exploiting the directional antilocality of these we complement the investigation of the emph{direct problem} with infinite data and single measurement uniqueness results for the associated emph{inverse problems}. Here, due to the only directional antilocality, new geometric conditions arise on the measurement domains. We discuss both the setting of symmetric and a particular class of non-symmetric nonlocal elliptic operators, and contrast the corresponding results for the direct and inverse problems. In particular for only one-sided operators new phenomena emerge both in the direct and inverse problems: For instance, it is possible to study the problem in data spaces involving local and nonlocal data, the unique continuation property may not hold in general and further restrictions on the measurement set for the inverse problem arise." @default.
- W3204546543 created "2021-10-11" @default.
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- W3204546543 date "2021-09-30" @default.
- W3204546543 modified "2023-10-18" @default.
- W3204546543 title "On the Calder'on problem for nonlocal Schrodinger equations with homogeneous, directionally antilocal principal symbols" @default.
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