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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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A matrix analysis approach to reproducing kernels
by
Jorge Buescu
Dep. Matemática, Instituto Superior Técnico
Coauthors: A. C. Paixão, ISEL

We consider holomorphic reproducing kernels on Cn. We show that their characterization as Moore matrices yields, by positive-semidefiniteness of the involved matrices, an n- parameter family of differential inequalities of which the order 0 case is the familiar diagonal dominance case. Similar inequalities are obtained for sufficiently smooth kernels in Rn. These inequalities are obtained in a strictly algebraic-analytical fashion, that is, directly in Cn through matrix analysis; in the reproducing kernel Hilbert space they correspond to a form of the Cauchy-Schwarz inequality. As an application we mention that these inequalities are critical in studying positive integral equations on unbounded domains, implying that the corresponding integral operators are spectrally exceptionally well-behaved.

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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-44.