Displaying similar documents to “Calogero-Moser spaces and an adelic W -algebra”

Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

Bakalov, B., Horozov, E., Yakimov, M. (1997)

Serdica Mathematical Journal

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This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral...

Proof of the Treves theorem on the KdV hierarchy

Leonid Dickey (2005)

Annales de l’institut Fourier

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A new, shorter, proof of the Treves theorem on an algebraic criterion for the first integrals of the KdV hierarchy is given, along with an addition to the theorem.

The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations

Luc Haine (2005)

Annales de l’institut Fourier

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The Stieltjes spectral matrix measure of the doubly infinite Jacobi matrix associated with a Toda g -soliton is computed, using Sato theory. The result is used to give an explicit expansion of the fundamental solution of some discrete heat equations, in a series of Jackson’s q -Bessel functions. For Askey-Wilson type solitons, this expansion reduces to a finite sum.

Propagation estimates for Dirac operators and application to scattering theory

Thierry Daudé (2004)

Annales de l’institut Fourier

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In this paper, we prove for a massive Dirac equation in flat spacetime. This allows us to construct the operator and to analyse its spectrum. Eventually, using this new information, we are able to obtain complete scattering results; that is to say we prove the existence and the asymptotic completeness of the Dollard modified wave operators.

Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators

Giancarlo Mauceri (1981)

Annales de l'institut Fourier

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We study the Riesz means for the eigenfunction expansions of a class of hypoelliptic differential operators on the Heisenberg group. The operators we consider are homogeneous with respect to dilations and invariant under the action of the unitary group. We obtain convergence results in L p norm, at Lebesgue points and almost everywhere. We also prove localization results.