<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Karlovich, Alexei Yu.</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">Joseph A. Ball</style></author><author><style face="normal" font="default" size="100%">Yuli Eidelman</style></author><author><style face="normal" font="default" size="100%">J. William Helton</style></author><author><style face="normal" font="default" size="100%">Vadim Olshevsky</style></author><author><style face="normal" font="default" size="100%">James Rovnyak</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Higher order asymptotic formulas for traces of Toeplitz matrices with symbols in Hölder-Zygmund spaces</style></title><secondary-title><style face="normal" font="default" size="100%">Recent Advances in Matrix and Operator Theory. Operator Theory: Advances and Applications, 179</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://link.springer.com/chapter/10.1007/978-3-7643-8539-2_11</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Bikhäuser</style></publisher><pub-location><style face="normal" font="default" size="100%">Basel</style></pub-location><pages><style face="normal" font="default" size="100%">185-196</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;/p&gt;
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