preprint
Inserted: 11 sep 2026
Last Updated: 11 sep 2026
Year: 2026
Abstract:
In our recent work FHS25, we introduced a numerical framework for approximating Sobolev functions on Wasserstein spaces from finite samples, leveraging structural properties established in FSS23. The present paper demonstrates that this methodology extends far beyond that specific setting. We identify a general class of metric measure spaces -- including weighted Riemannian manifolds and spaces of measures equipped with the Hellinger--Kantorovich distance -- for which the key hypotheses of Hilbertianity and the existence of a computable algebra of Lipschitz functions hold. Within this abstract framework, we recover and generalize the core approximation results of FHS25 for recovering functions from random point evaluations. Our main contribution is to show that the combination of theoretical foundations from FSS23 and algorithmic strategies from FHS25 is robust enough to apply to a wide variety of infinite-dimensional spaces of current interest.
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