Abstract
Recently, Borodin and Okounkov [2] established a remarkable identity for Toeplitz determinants. Two other proofs of this identity were subsequently found by Basor and Widom [1], who also extended the formula to the block case. We here give one more proof, also for the block case. This proof is based on a formula for the inverse of a finite block Toeplitz matrix obtained in the late seventies by Silbermann and the author.
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References
E.L. Basor and H. Widom: On a Toeplitz determinant identity of Borodin and Okounkov.Integral Equations Operator Theory 37 (2000), 397–401.
A. Borodin and A. Okounkov: A Fredholm determinant formula for Toeplitz determinants.Integral Equations Operator Theory 37 (2000), 386–396.
A. Böttcher and B. Silbermann: Notes on the asymptotic behavior of block Toeplitz matrices and determinants.Math. Nachr. 98 (1980), 183–210.
A. Böttcher and B. Silbermann:Analysis of Toeplitz Operators. Springer-Verlag, Berlin, Heidelberg, New York 1990.
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Böttcher, A. One more proof of the Borodin-Okounkov formula for Toeplitz determinants. Integr equ oper theory 41, 123–125 (2001). https://doi.org/10.1007/BF01202535
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DOI: https://doi.org/10.1007/BF01202535