- journal article metadata
European Mathematical Society Publishing House
2018-01-11 23:40:02
Zeitschrift für Analysis und ihre Anwendungen
Z. Anal. Anwend.
ZAA
0232-2064
1661-4534
Partial differential equations
Ordinary differential equations
Integral equations
Numerical analysis
10.4171/ZAA
http://www.ems-ph.org/doi/10.4171/ZAA
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2006)
37
2018
1
Propagation of Regularity and Positive Definiteness: a Constructive Approach
Jorge
Buescu
Universidade de Lisboa, Portugal
António
Paixão
Instituto Superior de Engenharia de Lisboa, Portugal
Claudemir
Oliveira
Universidade Federal de Itajubá, Brazil
Positive definite kernels, positive definite functions, differentiability, holomorphy, constructive approximation, exponentially convex functions
We show that, for positive definite kernels, if specific forms of regularity (continuity, $\mathcal{S}_n$-differentiability or holomorphy) hold locally on the diagonal, then they must hold globally on the whole domain of positive-definiteness. This local-to-global 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.
Fourier analysis
Real functions
Functions of a complex variable
1
24
10.4171/ZAA/1599
http://www.ems-ph.org/doi/10.4171/ZAA/1599
1
8
2018