The Mumford Dynamical System and the Gelfand–Dikii Recursion

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2024-04-01 DOI:10.1134/s0016266323040020

P. G. Baron

引用次数: 0

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.

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芒福德动力系统和格尔芬-迪基递归

摘要 Victor Buchstaber 在他的论文 "芒福德动力系统和超椭圆克莱因函数"[Funkts. Anal. Prilozhen.该理论的关键对象是他在论文中引入的 \((P,Q)\)- 递归。在本文中，我们进一步发展了 \((P,Q)\)- 递归理论，并描述了它与 Korteweg-de Vries 层次、Lenard 算子和 Gelfand-Dikii 递归的联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

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.