Asymptotics of a Class of Operator Determinants with Application to the Cylindrical Toda Equations
نویسنده
چکیده
Then qk(t) = log det (I +Kk)− log det (I +Kk−1) is a solution to the system of equations. If ρ is supported in the set of nth roots of unity then the solution is n-periodic in that qk+n = qk for all k. The main interest is in the limit t→ 0+, while the t→ ∞ asymptotics are straightforward. The asymptotics for the qk are known once those for the determinants are, and since ρ is arbitrary there is no loss of generality if one considers det (I + K0) only. The asymptotics for this were determined in [7] in what we call here the regular case. This is where the function
منابع مشابه
Asymptotics of a Class of Operator Determinants
In previous work of C. A. Tracy and the author asymptotic formulas were derived for certain operator determinants whose interest lay in the fact that quotients of them gave solutions to the cylindrical Toda equations. In the present paper we consider a more general class of operators which retain some of the properties of those cited and we find analogous asymptotics for the determinants.
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