A Fredholm determinant formula for Toeplitz determinants

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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.

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Classical Analysis and ODEs, Representation Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/78876

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9907165
 http://arxiv.org/abs/math/9907165

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arXiv