Revisiting the Anisotropic Fractional Calderón Problem

Abstract We revisit the source-to-solution anisotropic fractional Calderón problem introduced and analyzed in [22] and [21]. Using the extension interpretation of the fractional Laplacian from [55], we provide an alternative argument for the recovery of the heat and wave kernels from [22]. This shows that in the setting of the source-to-solution anisotropic fractional Calderón problem the heat and the (degenerate) elliptic extension approach give rise to equivalent perspectives and that each kernel can be recovered from the other. Moreover, we also discuss the Dirichlet-to-Neumann anisotropic source-to-solution problem. Last but not least, we relate the local and nonlocal source-to-solution Calderón problems.