Blambert, Parvatham: Ultraconvergence et singularités pour une classe de séries d'exponentielles

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Maurice Blambert; R. Parvatham
Ultraconvergence et singularités pour une classe de séries d'exponentielles
Annales de l'institut Fourier, 29 no. 1 (1979), p. 239-262, doi: 10.5802/aif.737
Article PDF | Reviews MR 81c:30008 | Zbl 0386.30001 | 1 citation in Cedram

Résumé - Abstract

G. L. Luntz had obtained the results on the overconvergence for exponential series with constant complex coefficients and for Taylor-Dirichlet series. Here, we have proved results on the overconvergence of our series of the type $\Sigma {\bf P}_n(s)$exp$(-s\lambda _n$, where the $\lambda _n$ are complex numbers and ${\bf P}_n(s)$ are polynomials. Further by using a theorem due to A. F. Leont’ev-G. P. Lapin on the interpolation of entire functions of exponential type with certain conditions on the values of these functions and their derivatives at certain points, we obtain results on the localisation of singular points of analytic functions defined by our series.

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