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5th International ISAAC Congress
July 25-30, 2005
Department of Mathematics and Informatics, University of Catania
Catania, Sicily, Italy

Organizers
International ISAAC Board, Local organizing committee: F. Nicolosi (chairman), S. Bonafede, V. Cataldo, P. Cianci, G.R. Cirmi, S. D'Asero, G. Fiorito, L. Giusti, S. Leonardi, P.E. Ricci

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Eigenvalues of positive definite kernels on unbounded domains
by
Jorge Buescu
Dep. Matemática, Instituto Superior Técnico
Coauthors: A. C. Paixão (ISEL)

We study eigenvalues of integral operators defined by positive definite kernels on unbounded real intervals. Under very mild assumptions on its behaviour on the diagonal, positivity implies this operator is compact and trace class. Positive definite kernels are reproducing kernels in a suitable space; as a consequence of this fact minimally smooth kernels satisfy a 2-parameter family of differential inequalities. These inequalities are critical to ensure that the corresponding integral operator on unbounded real domains has exceptionally good properties. In particular it is compact and its eigenvalue distribution may be calculated from L2 approximation methods, yielding sharper results than the more general methods of interpolation theory in Banach space.

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Date received: May 30, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # card-43.