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Series in Mittag-Leffler Functions: Inequalities and Convergent Theorems

Paneva-Konovska, Jordanka (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 30A10, 30B10, 30B30, 30B50, 30D15, 33E12In studying the behaviour of series, defined by means of the Mittag-Leffler functions, on the boundary of its domain of convergence in the complex plane, we prove Cauchy-Hadamard, Abel, Tauber and Littlewood type theorems. Asymptotic formulae are also provided for the Mittag-Leffler functions in the case of " values of indices that are used in the proofs of the convergence theorems for the considered series.

Sous-espaces fermés de séries universelles sur un espace de Fréchet

Quentin Menet (2011)

Studia Mathematica

We improve a result of Charpentier [Studia Math. 198 (2010)]. We prove that even on Fréchet spaces with a continuous norm, the existence of only one restrictively universal series implies the existence of a closed infinite-dimensional subspace of restrictively universal series.

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