On lacunary Toeplitz determinants

Abstract

By using Riemann--Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants ${\det }_N[c_{{\ell }_a-m_b}[f]]$ generated by holomorhpic symbols, where ${\ell }_a=a$ (resp. $m_b=b$) except for a finite subset of indices $a=h_1,\dots ,h_n$ (resp. $b=t_1,\dots ,t_r$). In addition to the usual Szegö asymptotics, our answer involves a determinant of size $n+r$.

arXiv comment11 pages

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