How regular are regular singularities?
type: Item
instance of: scholarly article
title: How regular are regular singularities?
DOI: 10.1007/978-3-030-84304-5_11
author: Herwig Hauser
publication date: 2022-11-11T00:00:00Z
review text: In this paper, the author proposes an abstract look at the works of Fuchs and Frobenius on the solutions of ordinary differential equations at regular singularities. Starting from the study of the solutions of very simple equations like \begin{align*} &x^2y''-3xy'+3y=0\\ &x^3y'''-4x^2y''+9xy'-9=0\\ &x^2y''-3xy'+3y+x^3y=0\\ &x^2y''-3xy'+3y+x^2y=0 \end{align*} the author introduces various tools and various fundamental results necessary to understand the solutions in the neighborhood of the singularity \(x=0\). In particular, he shows that all relevant informations on the structure of the solutions are contained in the initial form of the differential operator. For the entire collection see [Zbl 1478.11004].
reviewed by: Pascal Remy
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 32B05
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 7615268
zbMATH Keywords: regular singularities
zbMATH Keywords: ordinary differential equations
MaRDI profile type: Publication
full work available at URL: 978-3-030-84304-5 11
OpenAlex ID: W3209205437
cites work: Picard-Vessiot Extensions of Real Differential Fields
cites work: Perfect bases for differential equations
cites work: Q4486422
cites work: Q5638554
cites work: Q3915082
cites work: Q5640051
cites work: Jordan decomposition for a class of singular differential operators
cites work: Sur les points singuliers des équations différentielles
cites work: Differential Galois Theory through Riemann-Hilbert Correspondence
cites work: Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point
cites work: Q3596942
cites work: Q4790565
cites work: Q5343650
description: scientific article; zbMATH DE number 7615268