Buescu, JorgePaixão, AntónioOliveira, Claudemir2018-02-262018-02-262018BUESCU, Jorge; PAIXÃO, António; OLIVEIRA, Claudemir – Propagation of regularity and positive definiteness: a constructive approach. Zeitschrift fur Analysis und Ihre Anwendungen. ISSN 0232-2064. Vol. 37, N.º 1, (2018), pp. 1-240232-20641661-4534http://hdl.handle.net/10400.21/8131We 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.engPositive definite kernelsPositive definite functionsDifferentiabilityHolomorphyConstructive approximationExponentially convex functionsjournal article10.4171/ZAA/1599