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Toeplitz Determinants and Szegö's Formula
Published online by Cambridge University Press: 09 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 1969
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