KdV polynomials and \(\Lambda\)-operator
type: Item
instance of: scholarly article
title: KdV polynomials and \(\Lambda\)-operator
zbMATH Open document ID: 0849.34063
author: Mayumi Ohmiya
published in: Osaka Journal of Mathematics
publication date: 1996-11-14T00:00:00Z
review text: Let \(u(x)\) be a meromorphic function defined in a region of the complex plane \(C\). The author studies algebraic properties of the spectrum of the differential operator \(H(u) = - \partial^2 + u(x)\) with the help of the associated recursion operator \(\Lambda (u) = \partial^{-1} ({1 \over 2} u'(x) + u(x) \partial - {1 \over 4} \partial^3)\). This operator generates the infinite sequence of differential polynomials (KdV polynomials) by the recurrence formula \(Z_n (u) = \Lambda (u)Z_{n - 1} (u)\), \(n \in \mathbb{N}\), \(Z_0 (u) = 1\). The case when the \(C-\) vector space \(V(u) = \cup_{m \in \mathbb{Z}^+} CZ_m (u)\) has finite dimension is considered in detail. The author shows that in this case the essential part of the problem can be reduced to the study of some algebraic properties of \(\Lambda (u) \in \text{End} (V(u))\).
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34M99
zbMATH DE Number: 880179
zbMATH Keywords: \(\Lambda\)-algorithm
zbMATH Keywords: Ince's theorem
zbMATH Keywords: McKean-Trubowitz type
zbMATH Keywords: trace formula
zbMATH Keywords: KdV polynomials
zbMATH Keywords: complex plane
zbMATH Keywords: spectrum
zbMATH Keywords: differential operator
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 880179