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Mathematics > Functional Analysis

arXiv:0711.2248 (math)
[Submitted on 14 Nov 2007 (v1), last revised 25 Nov 2007 (this version, v2)]

Title:Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies

Authors:Mattia Cafasso
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Abstract: We propose a method for computing any Gelfand-Dickey tau function living in Segal-Wilson Grassmannian as the asymptotics of block Toeplitz determinant associated to a certain class of symbols. Also truncated block Toeplitz determinants associated to the same symbols are shown to be tau function for rational reductions of KP. Connection with Riemann-Hilbert problems is investigated both from the point of view of integrable systems and block Toeplitz operator theory. Examples of applications to algebro-geometric solutions are given.
Comments: 35 pages. Typos corrected, some changes in the introduction
Subjects: Functional Analysis (math.FA); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)
MSC classes: 37K10 (Primary), 47B35 (Secondary)
Cite as: arXiv:0711.2248 [math.FA]
  (or arXiv:0711.2248v2 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.0711.2248
Journal reference: Mathematical Physics, Analysis and Geometry. February 2008, Volume 11, Issue 1, pp 11-51
Related DOI: https://doi.org/10.1007/s11040-008-9038-7

Submission history

From: Mattia Cafasso [view email]
[v1] Wed, 14 Nov 2007 17:16:24 UTC (25 KB)
[v2] Sun, 25 Nov 2007 16:50:47 UTC (26 KB)
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