Publications

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2022
Karlovych, Oleksiy, and Eugene Shargorodsky. "Toeplitz operators with non-trivial kernels and non-dense ranges on weak Hardy spaces." Toeplitz Operators and Random Matrices. In Memory of Harold Widom. Operator Theory: Advances and Applications, vol. 289. Eds. Estelle Basor, Albrecht ¨Böttcher, and Torsten Ehrhardt. Birkhäuser, 2022. 463-476.
2021
Karlovich, Alexei. "Toeplitz operators between distinct abstract Hardy spaces." Extended Abstracts Fall 2019. Trends in Mathematics, vol 12. Eds. Abakumov E., Baranov A., Borichev A., Fedorovskiy K., and Ortega-Cerdà J. Cham: Birkhäuser, 2021. 105-112.
2017
Bini, Dario, Torsten Ehrhardt, Alexei Yu. Karlovich, and Ilya M. Spitkovsky(eds.) Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. The Albrecht Böttcher Anniversary Volume. Basel: Birkhäuser Basel, 2017.Website
2008
Karlovich, Alexei Yu. "Higher order asymptotic formulas for traces of Toeplitz matrices with symbols in Hölder-Zygmund spaces." Recent Advances in Matrix and Operator Theory. Operator Theory: Advances and Applications, 179. Eds. Joseph A. Ball, Yuli Eidelman, William J. Helton, Vadim Olshevsky, and James Rovnyak. Basel: Bikhäuser, 2008. 185-196. Abstract

We prove a higher order asymptotic formula for traces of finite block Toeplitz matrices with symbols belonging to Hölder-Zygmund spaces. The remainder in this formula goes to zero very rapidly for very smooth symbols. This formula refines previous asymptotic trace formulas by Szegő and Widom and complement higher order asymptotic formulas for determinants of finite block Toeplitz matrices due to Böttcher and Silbermann.