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- Propagation of regularity and positive definiteness: a constructive approachPublication . Buescu, Jorge; Paixão, António; Oliveira, ClaudemirWe show that, for positive de finite kernels, ifspecific forms of regularity (continuity, S-n-differentiability or holomorphy) hold locally on the diagonal, then they must hold globally on the whole domain of positive-definiteness. This local-toglobal propagation of regularity is constructively shown to be a consequence of the algebraic structure induced by the non-negativity of the associated bilinear forms up to order 5. Consequences of these results for topological groups and for positive definite and exponentially convex functions are explored.