Higher order asymptotics of Toeplitz determinants with symbols in weighted Wiener algebras

Wiener-hopf Determinants with Fisher-hartwig Symbols

With localization techniques one can obtain general limit theorems for Toeplitz determinants with Fisher-Hartwig singularities from the asymptotics for any symbol with one singularity of general type. There exists a family of these for which the determinants can be evaluated explicitly and their asymptotics determined. But for the Wiener-Hopf analogue, although there are likely analogous locali...

Relative Szegő asymptotics for Toeplitz determinants

In this paper we study the asymptotic behavior, as n → ∞, of ratios Dn(e hdμ)/Dn(dμ) of Toeplitz determinants defined by a measure μ and a sufficiently smooth function h. The approach we follow is based on the Verblunsky coefficients associated to μ. We prove that that the second order asymptotics depends on only few Verblunsky coefficients. In particular, we establish a relative version of the...

Classifying higher rank analytic Toeplitz algebras

To a higher rank directed graph (Λ, d), in the sense of Kumjian and Pask, 2000, one can associate natural noncommutative analytic Toeplitz algebras, both weakly closed and norm closed. We introduce methods for the classification of these algebras in the case of single vertex graphs.

Toeplitz operators with special symbols

Asymptotics of Higher Order Entropies

Higher order entropies are kinetic entropy estimators for fluid models. These quantities are quadratic in the velocity v and temperature T derivatives and have temperature dependent coefficients. We investigate asymptotic expansions of higher order entropies for incompressible flows in terms of the Knudsen ǫk and Mach ǫm numbers. The correspoding entropic inequalities are obtained when ‖ log T‖...