A Fredholm determinant formula for Toeplitz determinants
经典分析与常微分方程
2007-05-23 v1 表示论
摘要
We prove a formula expressing a general n by n Toeplitz determinant as a Fredholm determinant of an operator 1-K acting on l_2({n,n+1,...}), where the kernel K admits an integral representation in terms of the symbol of the original Toeplitz matrix. The proof is based on the results of one of the authors, see math.RT/9907127, and a formula due to Gessel which expands any Toeplitz determinant into a series of Schur functions. We also consider 3 examples where the kernel involves the Gauss hypergeometric function and its degenerations.
引用
@article{arxiv.math/9907165,
title = {A Fredholm determinant formula for Toeplitz determinants},
author = {Alexei Borodin and Andrei Okounkov},
journal= {arXiv preprint arXiv:math/9907165},
year = {2007}
}