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

Jean-Pierre Ramis, Yasutaka Sibuya (1994)

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 $x \frac{d \vec{y}}{d x} = {\vec{G}}_{0} (x) + [λ (x) + A_{0}] \vec{y} + x^{μ} \vec{G} (x, \vec{y}),$ the idea of our proof is to interpret a formal power series solution...

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

V. Swaminathan (1974)

Mathematische Zeitschrift

A note on the $[τ, f (x)]$ means

V. Swaminathan (1979)

Matematički Vesnik

A probabilistic description of the three theorems of Hardy.

Goonatilake, Rohitha (2002)

Southwest Journal of Pure and Applied Mathematics [electronic only]

A Tauberian theorem for Abelian summability methods.

D. Borwein, B. Watson (1976)

Journal für die reine und angewandte Mathematik

A tauberian theorem for Cesàro summability

B. Kuttner (1977)

Compositio Mathematica

Accelero-summation of the formal solutions of nonlinear difference equations

Geertrui Klara Immink (2011)

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...

Displaying 1 – 11 of 11

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

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

A note on the $[τ, f (x)]$ means

A probabilistic description of the three theorems of Hardy.

A Tauberian theorem for Abelian summability methods.

A tauberian theorem for Cesàro summability

Accelero-summation of the formal solutions of nonlinear difference equations

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

Addition au mémoire sur les séries divergentes

Application of a Tauberian theorem to finite model theory.

Approximation on the semi-infinite interval.

Currently displaying 1 – 11 of 11