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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 Generalization of the Prolate Spheroidal Wave Functions in Reproducing-Kernel Hilbert Spaces
by
Ahmed I. Zayed
DePaul University, Chicago, USA

Many systems of orthogonal polynomials and functions are bases of a variety of function spaces, such as the Hermite and Laguerre functions which are orthogonal bases of L2(-¥, ¥) and L(0, ¥), and the Jacobi polynomials which are an orthogonal basis of a weighted L2(-1, 1). The associated Legendre functions, and more generally, the spheroidal wave functions are also an orthogonal basis of L2(-1, 1). The prolate spheroidal wave functions, which are a special case of the spheroidal wave functions, possess a very surprising and unique property. They are an orthogonal basis of both L2(-1, 1) and a subspace of L2(-¥, ¥), known as the Paley-Wiener space of bandlimited functions. No other system of orthogonal functions is known to possess this strange property. This raises the question of whether there are other systems possessing this property. The aim of the talk is to answer this question in the affirmative by using ideas from the theory of reproducing-kernel Hilbert spaces as developed by S. Saitoh.

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Date received: June 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 # carf-42.