Norms of Toeplitz Matrices with Fisher-Hartwig Symbols

we call a the symbol of the sequence {Tn} and denote Tn by Tn(a). The case where a is in L∞(T) is easy, since then ‖Tn(a)‖ → ‖a‖∞ as n → ∞. Things are more complicated for a ∈ L(T) \L∞(T). We here focus our attention on so-called FisherHartwig symbols with a single singularity, that is, we consider functions a of the form a(t) = |t− t0|φβ,t0(t)b(t) (t ∈ T) where t0 ∈ T, α is a complex number subject to the constraint 0 < Reα < 1/2, β is a complex number satisfying −1/2 < Re β ≤ 1/2, φβ,t0 is defined as φβ,t0(t) = exp(iβ arg (−t/t0)) (t ∈ T)