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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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On functions of w-bounded type in the half-plane
by
Armen M. Jerbashian
Institute of Mathematics, National Academy of Sciences of Armenia

The lecture gives the basic representations of the general theory of functions of w-bounded type in the upper half-plane. The starting point are the canonical representations of some Banach spaces Apw, g of holomorphic functions. For p=2 (i.e. in the case of Hilbert spaces) there is a theorem on the orthogonal projection from the corresponding L2w to A2w, a Paley-Wiener type theorem and a theorem on a natural isometry between A2w and the Hardy space H2, which is an integral operator along with its inversion. Then the canonical representations of Nevanlinna-Djrbashian type classes of d-subharmonic functions are given. The functions from the considered spaces and classes can have arbitrary growth near the finite points of the real axis.

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Date received: April 15, 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 # capg-68.