6533b820fe1ef96bd1279938

RESEARCH PRODUCT

On lacunary Toeplitz determinants

Karol K. Kozlowski

subject

CombinatoricsGeneral MathematicsAsymptotic expansionLacunary functionToeplitz matrixMathematicsA determinant

description

By using Riemann--Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants $\det_N\big[ c_{\ell_a-m_b}[f] \big]$ 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 Szeg\"{o} asymptotics, our answer involves a determinant of size $n+r$.

https://doi.org/10.3233/asy-131210