Abstract

Motivated by the recent increase in interest in Toeplitz determinants of large order, whose elements are moments with respect to measures, by their connection with the theory of quantum gravity we have given exact values of the determinants for several large classes of measures. These classes are related to the continued fraction of Gauss and its q-extension. We have proven that the q-extension, which is related to the theory of quantum groups, is unique. In addition we have extended the work of Szegő from measures of finite support to a wide class of those with infinite support.

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