Hausdorff moments, Hardy spaces and power series

Details Hausdorff moments, Hardy spaces and power series Hausdorff moments, Hardy spaces and power series

2005-11-24

arxiv.org/abs/math/0511604v1

J. Math. Anal. Appl. 234 (1999), 265-286

Mathematics

Classical Analysis and ODEs

17 pages, 2 Postscript figures

Scientific paper

In this paper we consider power and trigonometric series whose coefficients are supposed to satisfy the Hausdorff conditions, which play a relevant role in the moment problem theory. We prove that these series converge to functions analytic in cut domains. We are then able to reconstruct the jump functions across the cuts from the coefficients of the series expansions by the use of the Pollaczek polynomials. We can thus furnish a solution for a class of Cauchy integral equations.

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