Stokes geometry of higher order linear ordinary differential equations and middle convolution
type: Item
instance of: scholarly article
title: Stokes geometry of higher order linear ordinary differential equations and middle convolution
zbMATH Open document ID: 1365.34149
author: Takahiro Moteki
author: Yoshitsugu Takei
published in: Advances in Mathematics
publication date: 2017-04-03T00:00:00Z
review text: The authors consider ordinary differential equations of the form \[ P\varphi (x,\eta )=\sum _{j=0}^na_j(x)(\eta ^{-1}\partial /\partial x)^j\varphi (x,\eta )=0, \] where \(\eta >0\) is a large parameter and \(a_j(x)\) are complex polynomials, \(a_n(x)\) is a nonzero constant. Such equations have formal (in general divergent) WKB solutions. In the case \(n=2\) these solutions can be Borel resummed in Stokes regions. The authors consider for \(n>2\) such equations which can be reduced to second order ones via middle convolution; this is a method introduced by Katz and developed by Dettweiler-Reiter, Oshima and others. The authors determine the complete Stokes geometry and explain how to obtain the Borel summability of the WKB solutions using the exact steepest descent method proposed by Aoki-Kawai-Takei.
Mathematics Subject Classification ID: 34M60
Mathematics Subject Classification ID: 34M03
Mathematics Subject Classification ID: 34M40
Mathematics Subject Classification ID: 34M30
zbMATH DE Number: 6699627
zbMATH Keywords: Stokes geometry
zbMATH Keywords: WKB solution
zbMATH Keywords: Borel summability
zbMATH Keywords: middle convolution
zbMATH Keywords: exact steepest descent method
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: j.aim.2017.02.006
OpenAlex ID: W2597029211
Wikidata QID: Q115362021
cites work: Q4693779
cites work: Q4849769
cites work: On the exact steepest descent method: a new method for the description of Stokes curves.
cites work: Q4663766
cites work: From divergent power series to analytic functions. Theory and application of multisummable power series
cites work: New Stokes’ line in WKB theory
cites work: Q3525815
cites work: Q4261277
cites work: Middle convolution of Fuchsian systems and the construction of rigid differential systems
cites work: Virtual Turning Points
cites work: Q3451867
cites work: Q5401237
cites work: Rigid Local Systems. (AM-139)
cites work: Q5716274
cites work: Q5401241
cites work: Fractional calculus of Weyl algebra and Fuchsian differential equations
cites work: Q3041568
DOI: 10.1016/J.AIM.2017.02.006
description: scientific article; zbMATH DE number 6699627