Publications

Export 5 results:
Sort by: Author [ Title (Asc)] Type Year
A B C D E F G [H] I J K L M N O P Q R S T U V W X Y Z   [Show ALL]
H
Karlovich, Alexei Yu. "Hardy-Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type." Studia Mathematica. 254.2 (2020): 149-178.
Karlovich, Alexei Yu. "Hardy-Littlewood maximal operator on the associate space of a Banach function space." Real Analysis Exchange. 44.1 (2019): 119-140.Website
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.

Karlovich, AY. "Higher order asymptotics of Toeplitz determinants with symbols in weighted Wiener algebras." Journal of Mathematical Analysis and Applications. 320.2 (2006): 944-963. AbstractWebsite

We extend a result of Bottcher and Silbermann on higher order asymptotics of determinants of block Toeplitz matrices with symbols in Wiener algebras with power weights to the case of Wiener algebras with general weights satisfying natural submultiplicativity, monotonicity, and regularity conditions.

Karlovich, Alexei Yu. "Higher-order asymptotic formulas for Toeplitz matrices with symbols in generalized Hölder spaces." Operator Algebra, Operator Theory and Applications. Operator Theory Advances and Applications, 181. Eds. MA Bastos, I. Gohberg, AB Lebre, and FO Speck. Basel: Birkhäuser, 2008. 207-228. Abstract

We prove higher-order asymptotic formulas for determinants and traces of finite block Toeplitz matrices generated by matrix functions belonging to generalized Hölder spaces with characteristic functions from the Bari-Stechkin class. We follow the approach of Böttcher and Silbermann and generalize their results for symbols in standard Hölder spaces.