Théorie des nombres et singularités.
Theta function identities from optical neural network transformations.
Topological and algebraic genericity of divergence and universality
We give general theorems which assert that divergence and universality of certain limiting processes are generic properties. We also define the notion of algebraic genericity, and prove that these properties are algebraically generic as well. We show that universality can occur with Dirichlet series. Finally, we give a criterion for the set of common hypercyclic vectors of a family of operators to be algebraically generic.
Über die Summierbarkeit von Dirichletreihen mit multiplikativen Koeffizienten.
Ueber eine Verallgemeinung der Taylorschen Reihe
Ultraconvergence et singularités pour une classe de séries d'exponentielles
Localisation des singularités des fonctions analytiques définies par des séries du type exp, où les sont complexes et où les sont des polynômes tayloriens, en utilisant des propriétés obtenues selon deux méthodes originellement dues l’une à B. Lepson pour les séries d’exponentielles à coefficients polynomiaux et dont la suite des exposants est une -suite et l’autre à G. L. Luntz pour les séries de Taylor-Dirichlet. Le résultat fondamental utilise un théorème de A. F. Leont’ev-G. P. Lapin...
Un Théorème sur les Séries de Dirichlet.
Universal approximation theorem for Dirichlet series.
Universal Taylor series
We strengthen a result of Chui and Parnes and we prove that the set of universal Taylor series is a -dense subset of the space of holomorphic functions defined in the open unit disc. Our result provides the answer to a question stated by S.K. Pichorides concerning the limit set of Taylor series. Moreover, we study some properties of universal Taylor series and show, in particular, that they are trigonometric series in the sense of D. Menchoff.
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Zeros and poles of Dirichlet series
Under certain mild analytic assumptions one obtains a lower bound, essentially of order , for the number of zeros and poles of a Dirichlet series in a disk of radius . A more precise result is also obtained under more restrictive assumptions but still applying to a large class of Dirichlet series.
Zeta functions for the Riemann zeros
A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.
Zobecnění Taylorova a Laurentova rozvoje
Zur Theorie der Dirichlet'schen Reihen
Аналоги теоремы Вимана для рядов Дирихле
Аппроксимация однородных субгармонических функций
Замечание о коэффициентах ряда Лорана дзета-функции Римана
Инвариантные подпространства пространства
Интегральное представление для суммы степенного ряда и полиномиальные разложения.
Интерпретация теоремы Берлинга-Мальявена о радиусе полноты