I think it would have been worth mentioning! Analytics continuation always stays in the original manifold and thus doesn’t extend into another dimension. It is true, though, that the local extension can lead to Riemann surfaces that can eventually “wrap around” and form “layers” that have multiple different value at the same original coordinate. This can be interpreted as pointing into another dimension (even though it is not doing so continuously (real-values)). I would guess there is a subset of methods for Hyperpolation that use this approach to hyperpolate some functions (maybe for functions for which analytical continuation isn’t known yet).
I’m surprised that the paper doesn’t mention analytic continuations of complex functions—maybe that is also taken as an instance of extrapolation?
I think it would have been worth mentioning! Analytics continuation always stays in the original manifold and thus doesn’t extend into another dimension. It is true, though, that the local extension can lead to Riemann surfaces that can eventually “wrap around” and form “layers” that have multiple different value at the same original coordinate. This can be interpreted as pointing into another dimension (even though it is not doing so continuously (real-values)). I would guess there is a subset of methods for Hyperpolation that use this approach to hyperpolate some functions (maybe for functions for which analytical continuation isn’t known yet).