Asymptotics of a Class of Operator Determinants
نویسنده
چکیده
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.
منابع مشابه
Asymptotics of a Class of Operator Determinants with Application to the Cylindrical Toda Equations
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 i...
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تاریخ انتشار 2008