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Toeplitz Determinants and Szegö's Formula

Published online by Cambridge University Press:  09 April 2009

R. E. Hartwig
R. E. Hartwig
Affiliation:
The University of AdelaideAdelaide
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Abstract

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In this paper the Toeplitz determinant of order s ≧ 1 generated by the rational function , with , and , is evaluated exactly for all values of s ≧ m, as , where in with and , thus proving Szegö's formula for the function fm, n(z).

By forming the rational approximation of the generating function the formula is then extended to enabling the evaluation of the limit of Toeplitz determinants generated by certain classes of complex valued functions.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 1-2 , February 1969 , pp. 62 - 99
Copyright
Copyright © Australian Mathematical Society 1969

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