@inbook {7482,
	title = {Higher order asymptotic formulas for traces of Toeplitz matrices with symbols in H{\"o}lder-Zygmund spaces},
	booktitle = {Recent Advances in Matrix and Operator Theory. Operator Theory: Advances and Applications, 179},
	year = {2008},
	pages = {185-196},
	publisher = {Bikh{\"a}user},
	organization = {Bikh{\"a}user},
	address = {Basel},
	abstract = {<p>We prove a higher order asymptotic formula for traces of finite block Toeplitz matrices with symbols belonging to H{\"o}lder-Zygmund spaces. The remainder in this formula goes to zero very rapidly for very smooth symbols. This formula refines previous asymptotic trace formulas by Szeg{\H o} and Widom and complement higher order asymptotic formulas for determinants of finite block Toeplitz matrices due to B{\"o}ttcher and Silbermann.</p>
},
	url = {http://link.springer.com/chapter/10.1007/978-3-7643-8539-2_11},
	author = {Karlovich, Alexei Yu.},
	editor = {Joseph A. Ball and Yuli Eidelman and J. William Helton and Vadim Olshevsky and James Rovnyak}
}
