A generalization of a result of André-Jeannin concerning summation of reciprocals.
A note on matrix transformations of holomorphic Dirichlet series.
A note on the construction of the proximate type of an entire Dirichlet series with index-pair
A remark on the means of entire Dirichlet series
A study of various results for a class of entire Dirichlet series with complex frequencies
Let be a class of entire functions represented by Dirichlet series with complex frequencies for which is bounded. Then is proved to be a commutative Banach algebra with identity and it fails to become a division algebra. is also proved to be a total set. Conditions for the existence of inverse, topological zero divisor and continuous linear functional for any element belonging to have also been established.
Absolutely convergent Dirichlet series and analytic continuation of its sum.
Addendum to the paper " On the zeros of a class of generalized Dirichlet series".
An algorithm for nonharmonic signal analysis using Dirichlet series on convex polygons.
An estimate for the Dirichlet series in a half-strip in the case of the irregular distribution of exponents. II.
An estimate for the Dirichlet series with Fejér gaps on the real axis.
Analytic continuation of Dirichlet series.
The questions considered in this paper arose from the study [KS] of I. Fredholm's (insufficient) proof that the gap series Σ0∞ an ζn2 (where 0 < |a| < 1) is nowhere continuable across {|ζ| = 1}. The interest of Fredholm's method ([F],[ML]) is not so much its efficacy in proving gap theorems (indeed, much more general results can be got by other means, cf. the Fabry gap theorem in [Di]) as in the connection it made between certain special gap series and partial differential equations...
Applications arithmétiques de l'étude des valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme
Nous étudions les fonctions -adiques associées à des séries du typedans certains cas, où elles admettent un prolongement méromorphe à avec un nombre fini de pôles et des valeurs aux entiers négatifs algébriques. On retrouve comme cas particulier les fonctions -adiques des corps totalement réels et les fonctions -multiples -adiques.
Arithmetic mean function of the real part of entire Dirichlet series I
Arithmetical properties of finite rings and algebras, and analytical number theory. V. Categories and relative analytic number theory.
-stability of the maximal term of the Hadamard composition of two Dirichlet series.
Characterization of bases in the space of entire Dirichlet series of order zero
Coefficient multipliers on spaces of vector-valued entire Dirichlet series
The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some...
Coherent states and frames in the Bargman space of entire functions.
Composition operators in the Dirichlet series setting
In this work, we begin with a survey of composition operators on the Hardy space H² and on the Wiener algebra A⁺ of absolutely convergent Taylor series, with special emphasis on their compactness, or invertibility, or isometric character. The main results are due respectively to J. Shapiro and D.~Newman. In a second part, we present more recent results, due to Gordon and Hedenmalm on the one hand, and to Bayart, the author et al. on the other hand, concerning the analogues of H² and A⁺ in the setting...
Continuity on the Boundary and Analytic Continuation of Continued Fractions.