Analytic continuation by means of the methods of divergent series
Analytic continuation for some classes of separately analytic functions of real variables
For functions that are separately solutions of an elliptic homogeneous PDE with constant coefficients, we prove an analogue of Siciak's theorem for separately holomorphic functions.
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...
Analytic continuation of functions difined by means of continued fraction.
Application of differential equations for transforming the implicit functions into the explicit ones
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.
Applications of a special representation of analytic functions.
Approximants de Padé-Hermite. 1ère partie: théorie.
Approximants de Padé-Hermite. 2ème partie: programmation.
Approximation of entire functions of slow growth.
Approximation of entire functions of slow growth on compact sets
In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth have been obtained in terms of approximation and interpolation errors.
Approximation of entire functions of two complex variables in Banach spaces.
Approximation par des fonctions holomorphes à croissance contrôlée.
Let Ω be a bounded pseudo-convex domain in Cn with a C∞ boundary, and let S be the set of strictly pseudo-convex points of ∂Ω. In this paper, we study the asymptotic behaviour of holomorphic functions along normals arising from points of S. We extend results obtained by M. Ortel and W. Schneider in the unit disc and those of A. Iordan and Y. Dupain in the unit ball of Cn. We establish the existence of holomorphic functions of given growth having a "prescribed behaviour" in almost all normals arising...
Areas of Projections of Analytic Sets.
Arithmetic mean function of the real part of entire Dirichlet series I
Arithmetic operations with regular C-fractions.
Arithmetical properties of finite rings and algebras, and analytical number theory. V. Categories and relative analytic number theory.
Asymptotic estimates for some number-theoretic power series
Asymptotic expansions of quasiperiodic solutions
Asymptotic FitzGerald inequalities.