Calcul de facteurs déterminants. (The calculation of determining factors)
type: Item
instance of: scholarly article
title: Calcul de facteurs déterminants. (The calculation of determining factors)
zbMATH Open document ID: 0675.34004
DOI: 10.1016/0022-0396(88)90152-0
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: Let \({\mathcal L}=D^ n+\sum^{n}_{i=0}a_ iD^ i\), \((a_ i\in K)\), be a differential operator with coefficients in the ring K of the series with complex coefficients. A Theorem by Hukuhara and Turrittin states the existence of a generating family of n independent solutions of \({\mathcal L}\), \(u_ i(t)=\exp Q_ i(t)t^{\lambda_ i}v_ i(t)\), where \(Q_ i\) is a polynomial in \(t^{-1/e}(e\in {\mathbb{N}})\), \(i=1,...,n\). The \(Q_ i\) are the determining factors of \({\mathcal L}\). The purpose of this paper is to provide a direct formula for the \(Q_ i\), as opposed to algorithmic computations going together with proofs of Hukuhara and Turrittin theorem. It is done here in the case of operators \({\mathcal L}\) of order \(\leq 3\). A same result was previously obtained by B. Helffer and Y. Kannai for the case of double characteristics.
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 4105360
zbMATH Keywords: multiple characteristics
zbMATH Keywords: determining factors
author: Johan Yebbou
reviewed by: Ovide Arino
MaRDI profile type: Publication
full work available at URL: 0022-0396(88)90152-0
OpenAlex ID: W2012538004
cites work: Q5179731
cites work: Q5843703
cites work: Lemmes de Hensel pour les opérateurs différentiels. Application à la reduction formelle des équations différentielles
cites work: Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point
cites work: Q5343650
description: scientific article; zbMATH DE number 4105360