Toeplitz Determinants and Szegö's Formula
- 1 February 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 9 (1-2) , 62-99
- https://doi.org/10.1017/s1446788700005668
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.Keywords
This publication has 1 reference indexed in Scilit:
- A Convergence Equivalence Related to Polynomials Orthogonal on the Unit CircleTransactions of the American Mathematical Society, 1961