Solvability of Difference Riccati Equations

Journal of Mathematical Sciences

Nishioka, Seiji¹ 

关键词: Cartan decomposition;    visible action;    symmetric space;    herringbone stitch;    spherical variety.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

WegeneralizeFranke'sgeneralizedLiouvillianextensionandKarr's$PiSigma$-extension,andstudysolvabilityofdifferenceRiccatiequations.Wedefinethedifferencefieldextensionsofvaluationringtypeandprovethefollowing.IfadifferenceRiccatiequationwhichdoesnotturnouttobelinearbyiterationshasasolutioninsomedifferencefieldextensionofvaluationringtype,thenoneoftheiteratedRiccatiequationshasanalgebraicsolution.Applyingthistheorem,weconcludeunsolvabilityofthe$q$-Airyequationandthe$q$-Besselequation.

【 授权许可】

Unknown