Revisiting the Anisotropic Fractional Calderón Problem

We revisit the source-to-solution anisotropic fractional Calder & oacute;n 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 Calder & oacute;n 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 Calder & oacute;n problems.