On Asymptotics of Toeplitz Determinants with Symbols of Nonstandard Smoothness

Abstract

We prove Szegő's strong limit theorem for Toeplitz determinants with a symbol having a nonstandard smoothness. We assume that the symbol belongs to the Wiener algebra and, moreover, the sequences of Fourier coefficients of the symbol with negative and nonnegative indices belong to weighted Orlicz classes generated by complementary N-functions both satisfying the 0 2 -condition and by weight sequences satisfying some regularity and compatibility conditions.

Analysis of Toeplitz Operators

“…The maximal 558 10 Toeplitz Determinants ideal space of W ∩ F Φ,Ψ ϕ,ψ can be identified with T. Therefore, an analogue of Corollary 6.55 is valid for W ∩ F Φ,Ψ ϕ,ψ . Following ideas of the proof of Corollary 10.45, A. Karlovich and P. Santos [303] obtained the following generalization of it.…”

“…Karlovich and P. Santos [303] also constructed a function such that the above result is applicable to it, but Corollary 10.45 is not.…”