Page 1 Next

Displaying 1 – 20 of 81

Showing per page

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 d y d x = G 0 ( x ) + λ ( x ) + A 0 y + x μ G ( x , y ) , the idea of our proof is to interpret a formal power series solution...

Addendum to: "Sequences of 0's and 1's" (Studia Math. 149 (2002), 75-99)

Johann Boos, Toivo Leiger (2005)

Studia Mathematica

There is a nontrivial gap in the proof of Theorem 5.2 of [2] which is one of the main results of that paper and has been applied three times (cf. [2, Theorem 5.3, (G) in Section 6, Theorem 6.4]). Till now neither the gap has been closed nor a counterexample found. The aim of this paper is to give, by means of some general results, a better understanding of the gap. The proofs that the applications hold will be given elsewhere.

Calculations in new sequence spaces

Bruno de Malafosse (2007)

Archivum Mathematicum

In this paper we define new sequence spaces using the concepts of strong summability and boundedness of index p > 0 of r -th order difference sequences. We establish sufficient conditions for these spaces to reduce to certain spaces of null and bounded sequences.

Currently displaying 1 – 20 of 81

Page 1 Next