{"title":"芒福德动力系统和格尔芬-迪基递归","authors":"P. G. Baron","doi":"10.1134/s0016266323040020","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In his paper “The Mumford dynamical system and hyperelliptic Kleinian functions” [Funkts. Anal. Prilozhen. <b>57</b> (4), 27–45 (2023)] Victor Buchstaber developed the differential-algebraic theory of the Mumford dynamical system. The key object of this theory is the <span>\\((P,Q)\\)</span>-recursion introduced in his paper. </p><p> In the present paper, we further develop the theory of the <span>\\((P,Q)\\)</span>-recursion and describe its connections to the Korteweg–de Vries hierarchy, the Lenard operator, and the Gelfand–Dikii recursion. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Mumford Dynamical System and the Gelfand–Dikii Recursion\",\"authors\":\"P. G. Baron\",\"doi\":\"10.1134/s0016266323040020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> In his paper “The Mumford dynamical system and hyperelliptic Kleinian functions” [Funkts. Anal. Prilozhen. <b>57</b> (4), 27–45 (2023)] Victor Buchstaber developed the differential-algebraic theory of the Mumford dynamical system. The key object of this theory is the <span>\\\\((P,Q)\\\\)</span>-recursion introduced in his paper. </p><p> In the present paper, we further develop the theory of the <span>\\\\((P,Q)\\\\)</span>-recursion and describe its connections to the Korteweg–de Vries hierarchy, the Lenard operator, and the Gelfand–Dikii recursion. </p>\",\"PeriodicalId\":575,\"journal\":{\"name\":\"Functional Analysis and Its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Functional Analysis and Its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0016266323040020\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Functional Analysis and Its Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0016266323040020","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Mumford Dynamical System and the Gelfand–Dikii Recursion
Abstract
In his paper “The Mumford dynamical system and hyperelliptic Kleinian functions” [Funkts. Anal. Prilozhen. 57 (4), 27–45 (2023)] Victor Buchstaber developed the differential-algebraic theory of the Mumford dynamical system. The key object of this theory is the \((P,Q)\)-recursion introduced in his paper.
In the present paper, we further develop the theory of the \((P,Q)\)-recursion and describe its connections to the Korteweg–de Vries hierarchy, the Lenard operator, and the Gelfand–Dikii recursion.
期刊介绍：
Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.
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