On the limit of block Toeplitz determinants
On the limit of block Toeplitz determinants
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论块托普利茨行列式的极限
DOI：
10.1090/s0002-9939-1975-0370254-4
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发表时间：
1975
期刊：
影响因子：
--
通讯作者：
H. Widom
中科院分区：
文献类型：
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作者：
H. Widom
块Toeplitz行列式的一个渐近公式，推广了Szeg6的著名公式为普通Toeplitz行列式。本文的前身[5]关注的是块Toeplitz行列式DN[.]的极限行为。= det TNh[01其中TN[s] =（sb.X），i，j= 0，*？，N.这里+（Z）=k E Xk l z| =1是一个r x r矩阵值函数，满足
An asymptotic formula is derived for block Toeplitz determinants which generalizes Szeg6's well-known formula for ordinary Toeplitz determinants. The predecessor of this paper [5] was concerned, among other things, with the limiting behavior of the block Toeplitz determinants DN[.] = det TNh[01 where TN[s] = (sb.X), i, j= 0, *?, N. Here +(Z) =k E Xk l z |=1 is an r x r matrix-valued function satisfying