Original Articles

The generalized functions of the second kind for general exponential weights

Published in: Quaestiones Mathematicae
Volume 33 , issue 4 , 2010 , pages: 477–484

DOI: 10.2989/16073606.2010.541622

Author(s): H.P. Mashele Centre for Business Mathematics and Informatics, South Africa

Keywords: 41A05 , 41A10 , 41A17 , 41A65 , 41A05 , 41A10 , 41A17 , 41A65

Abstract

Let I be a finite or infinite interval containing 0, and let W : I → (0, ∞). Assume that W ² is a weight, so that we may define orthonormal polynomials corresponding to W ². The generalized functions of the second kind are , where H denotes the Hilbert transform, and v the bounded function on I. We investigate boundedness of the sum of q_j (W ², v, x)² for the general class of exponential weights.

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