Page 1 Next

## Displaying 1 – 20 of 61

Showing per page

### A new proof of multisummability of formal solutions of non linear meromorphic differential equations

Annales de l'institut Fourier

We give a new proof of multisummability of formal power series solutions of a non linear meromorphic differential equation. We use the recent Malgrange-Ramis definition of multisummability. The first proof of the main result is due to B. Braaksma. Our method of proof is very different: Braaksma used Écalle definition of multisummability and Laplace transform. Starting from a preliminary normal form of the differential equation$x\frac{d\stackrel{\to }{y}}{dx}={\stackrel{\to }{G}}_{0}\left(x\right)+\left[\lambda \left(x\right)+{A}_{0}\right]\stackrel{\to }{y}+{x}^{\mu }\stackrel{\to }{G}\left(x,\stackrel{\to }{y}\right),$the idea of our proof is to interpret a formal power series solution...

### A Note on the Family F (a, q) of Summability Methods.

Mathematische Zeitschrift

### A note on the $\left[\tau ,f\left(x\right)\right]$ means

Matematički Vesnik

### A probabilistic description of the three theorems of Hardy.

Southwest Journal of Pure and Applied Mathematics [electronic only]

### A Tauberian theorem for Abelian summability methods.

Journal für die reine und angewandte Mathematik

### A tauberian theorem for Cesàro summability

Compositio Mathematica

### Accelero-summation of the formal solutions of nonlinear difference equations

Annales de l’institut Fourier

In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of “level ${1}^{+}$”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum...

### Addendum to: Iteration Products of Methods of Summability and Natural Scales.

Manuscripta mathematica

### Addition au mémoire sur les séries divergentes

Annales scientifiques de l'École Normale Supérieure

### Application of a Tauberian theorem to finite model theory.

Archiv für mathematische Logik und Grundlagenforschung

### Approximation on the semi-infinite interval.

International Journal of Mathematics and Mathematical Sciences

### Borel matrix

Commentationes Mathematicae Universitatis Carolinae

We study the Borel summation method. We obtain a general sufficient condition for a given matrix $A$ to have the Borel property. We deduce as corollaries, earlier results obtained by G. M“uller and J.D. Hill. Our result is expressed in terms belonging to the theory of Gaussian processes. We show that this result cannot be extended to the study of the Borel summation method on arbitrary dynamical systems. However, in the ${L}^{p}$-setting, we establish necessary conditions of the same kind by using Bourgain’s...

### Borel summability beyond the factorial growth

Annales de l'I.H.P. Physique théorique

### Borel summation and splitting of separatrices for the Hénon map

Annales de l’institut Fourier

We study two complex invariant manifolds associated with the parabolic fixed point of the area-preserving Hénon map. A single formal power series corresponds to both of them. The Borel transform of the formal series defines an analytic germ. We explore the Riemann surface and singularities of its analytic continuation. In particular we give a complete description of the “first” singularity and prove that a constant, which describes the splitting of the invariant manifolds, does not vanish. An interpretation...

### Corrigendum: On $\left(J,{p}_{n}\right)$ summability of Fourier series.

International Journal of Mathematics and Mathematical Sciences

### Die allgemeine Form der O-Tauber-Bedingung für das Euler-Knopp- und Borel-Verfahren.

Journal für die reine und angewandte Mathematik

### Distributional versions of Littlewood's Tauberian theorem

Czechoslovak Mathematical Journal

We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel...

### Equivalence results for discrete Abel means.

International Journal of Mathematics and Mathematical Sciences

### Fonctions multisommables

Annales de l'institut Fourier

La notion de multisommabilité intervient dans la théorie des équations différentielles lorsque des exponentielles d’ordres différents se mélangent. Elle a été introduite par J. Écalle et étudié récemment par plusieurs auteurs. On en donne ici une définition simple, qui fait uniquement intervenir des propriétés de décroissance exponentielle.

### Fondements de la théorie des séries divergentes sommables

Journal de Mathématiques Pures et Appliquées

Page 1 Next