On the Gelfand-Hille theorems
On the overconvergence of certain series.
Polylogarithms and arithmetic function spaces
Polynomial approximations and universality
We give another version of the recently developed abstract theory of universal series to exhibit a necessary and sufficient condition of polynomial approximation type for the existence of universal elements. This certainly covers the case of simultaneous approximation with a sequence of continuous linear mappings. In the case of a sequence of unbounded operators the same condition ensures existence and density of universal elements. Several known results, stronger statements or new results can be...
Power-bounded elements and radical Banach algebras
Firstly, we give extensions of results of Gelfand, Esterle and Katznelson--Tzafriri on power-bounded operators. Secondly, some results and questions relating to power-bounded elements in the unitization of a commutative radical Banach algebra are discussed.
Quantitative versions of a result of Hecke in the theory of uniform distribution mod 1
Radial limits of functions of slow growth in the unit disk.
Resommation des series formelles. Solutions d'équations différentielles linéaires ordinaires du second ordre dans le champ complexe au voisinage de singularités irrégulières.
Series in Mittag-Leffler Functions: Inequalities and Convergent Theorems
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.
Some gap power series in multidimensional setting
We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.
Sur les points singuliers d'une série de Taylor
Sur les séries de Taylor admettant leur cercle de convergence comme coupure
Sur les séries de Taylor et les transformations de Möbius.
Sur les singularités des séries de Taylor
The cliff of a Taylor polynomial. (La falaise d'un polynôme de Taylor.)
Theorems on the Convergence of Series in Generalized Lommel-Wright Functions
Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20The classical Cauchy-Hadamard, Abel and Tauber theorems provide useful information on the convergence of the power series in complex plane. In this paper we prove analogous theorems for series in the generalized Lommel-Wright functions with 4 indices. Results for interesting special cases of series involving Bessel, Bessel-Maitland, Lommel and Struve functions, are derived.We provide also a new asymptotic formula for the generalized ...
Transcendence results on the generating functions of the characteristic functions of certain self-generating sets
This article continues two papers which recently appeared in this same journal. First, Dilcher and Stolarsky [140 (2009)] introduced two new power series, F(z) and G(z), related to the so-called Stern polynomials and having coefficients 0 and 1 only. Shortly later, Adamczewski [142 (2010)] proved, inter alia, that G(α),G(α⁴) are algebraically independent for any algebraic α with 0 < |α| < 1. Our first key result is that F and G have large blocks of consecutive zero coefficients. Then, a Roth-type...
Über die Invarianz der absoluten Kovergenz bei konformer Abbildung.
Über eine Methode von E. Hecke in der Theorie der Gleichverteilung
Über gewisse nichtfortsetzbare Potenzreihen.