Holomorphic extension associated with Fourier-Legendre expansions

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In this article we prove that if the coefficients of a Fourier-Legendre expansion satisfy a suitable Hausdorff-type condition, then the series converges to a function which admits a holomorphic extension to a cut-plane. Furthermore, we prove that a Laplace-type (Laplace composed with Radon) transform of the function describing the jump across the cut is the unique Carlsonian interpolation of the Fourier coefficients of the expansion. We can thus reconstruct the discontinuity function from the coefficients of the Fourier-Legendre series by the use of the Pollaczek polynomials.
19 pages, 2 Postiscript figures

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Classical Analysis and ODEs, Complex Variables, 30B40; 30B50; 30C10; 42C10

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http://salesiana.dossiersoluciones.com/handle/123456789/106105

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0512121
 http://arxiv.org/abs/math/0512121
 J. Geom. Anal. 12 (2002), 355-374

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arXiv