Hausdorff Moments, Hardy Spaces, and Power Series
Copyright policy )Hausdorff Moments, Hardy Spaces, and Power Series
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.
17 pages, 2 Postscript figures
- National Research Council Italy
- National Institute for Nuclear Physics Italy
- University of Genoa Italy
- National Research Council Sri Lanka
Pollaczek polynomials, Mathematics - Complex Variables, 30B10; 30E05, Applied Mathematics, 30B10, Moment problems and interpolation problems in the complex plane, Approximation in the complex plane, Mathematics - Classical Analysis and ODEs, 30E05, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Complex Variables (math.CV), Analysis
Pollaczek polynomials, Mathematics - Complex Variables, 30B10; 30E05, Applied Mathematics, 30B10, Moment problems and interpolation problems in the complex plane, Approximation in the complex plane, Mathematics - Classical Analysis and ODEs, 30E05, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Complex Variables (math.CV), Analysis
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