Mathematics – Classical Analysis and ODEs
Scientific paper
2005-12-06
J. Geom. Anal. 12 (2002), 355-374
Mathematics
Classical Analysis and ODEs
19 pages, 2 Postiscript figures
Scientific paper
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.
Micheli Enrico de
Viano Giovanni Alberto
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