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Seminar on Complex Analysis (Gonchar Seminar)
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Szegő theorem and tau functions A. V. Domrin Lomonosov Moscow State University |
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Abstract: We show that the constant term (the first non-trivial term) in the Szegő–Widom asymptotic formula for the determinants of certain special truncated block-Toeplitz matrices (loops) is the tau function for the solution (corresponding to this loop) of a soliton equation of parabolic type. We discuss consequences of this fact concerning the analytic properties of local holomorphic solutions of such equations. |
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