Differential equations on the Prym theta function. A realness criterion for two-dimensional finite-zone potential Schrödinger operators
type: Item
instance of: scholarly article
title: Differential equations on the Prym theta function. A realness criterion for two-dimensional finite-zone potential Schrödinger operators
zbMATH Open document ID: 0806.35022
DOI: 10.1007/BF01077068
publication date: 1993-01-16T00:00:00Z
review text: This article deals with finite-zone two-dimensional Schrödinger operators of the type \[ L = {\partial^ 2 \over \partial z \partial \overline z} + 2{\partial^ 2 \over \partial z \partial \overline z} \theta_{Pr} (zu^ 1 + \overline zu^ 2-e) - \varepsilon_ 0 \] where \(e,u^ 1,u^ 2 \in {\mathcal C}^ 2\) and \(\theta_{Pr}\) -- Prym theta- function of a complex algebraic curve \(P\) of genus \(2g\). The main result is the following: the reality of the function \(u = {\partial^ 2 \over \partial z \partial \overline z} \theta_{Pr} (zu^ 1 + \overline zu^ 2-e) - \varepsilon_ 0\) implies the reality of the curve \(P\).
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 14H42
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 95220
zbMATH Keywords: Prym theta-function
author: Sergey Natanzon
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 95220