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Orientador(es)
Resumo(s)
We 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.
Descrição
Palavras-chave
Positive definite kernels Positive definite functions Differentiability Holomorphy Constructive approximation Exponentially convex functions
Contexto Educativo
Citação
BUESCU, 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. 1-24
Editora
European Mathematical Society