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15 March 2003 Dispersionless Toda and Toeplitz operators
A. Bloch, F. Golse, T. Paul, A. Uribe
Duke Math. J. 117(1): 157-196 (15 March 2003). DOI: 10.1215/S0012-7094-03-11713-5

Abstract

In this paper we present some results on the dispersionless limit of the Toda lattice equations viewed as the semiclassical limit of an equation involving certain Toeplitz operators. We consider both nonperiodic and periodic boundary conditions. For the nonperiodic case the phase space is the Riemann sphere, while in the periodic case it is the torus $\mathbb {C}/\mathbb {Z}\sp 2$. In both cases we prove precise estimates on the dispersionless limit. In addition, we show that the Toda equations, although they are nonlinear, propagate a Toeplitz operator into an operator arbitrarily close to a Toeplitz operator as long as the Toda partial differential equation (PDE) (dispersionless limit) admits smooth solutions.

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A. Bloch. F. Golse. T. Paul. A. Uribe. "Dispersionless Toda and Toeplitz operators." Duke Math. J. 117 (1) 157 - 196, 15 March 2003. https://doi.org/10.1215/S0012-7094-03-11713-5

Information

Published: 15 March 2003
First available in Project Euclid: 26 May 2004

zbMATH: 1024.37047
MathSciNet: MR1962785
Digital Object Identifier: 10.1215/S0012-7094-03-11713-5

Subjects:
Primary: 37K60
Secondary: 35P20, 47B35

Rights: Copyright © 2003 Duke University Press

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Vol.117 • No. 1 • 15 March 2003
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