A Fredholm determinant formula for Toeplitz determinants
Copyright policy )A Fredholm determinant formula for Toeplitz determinants
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.
- University of California, Berkeley United States
- University of Pennsylvania United States
- THE UNIVERSITY OF CHICAGO United States
Fredhom determinant, Toeplitz determinants, Toeplitz matrix, Classical hypergeometric functions, \({}_2F_1\), Toeplitz operator, Mathematics - Classical Analysis and ODEs, Toeplitz operators, Hankel operators, Wiener-Hopf operators, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), Classical Analysis and ODEs (math.CA), FOS: Mathematics, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Representation Theory (math.RT), Mathematics - Representation Theory
Fredhom determinant, Toeplitz determinants, Toeplitz matrix, Classical hypergeometric functions, \({}_2F_1\), Toeplitz operator, Mathematics - Classical Analysis and ODEs, Toeplitz operators, Hankel operators, Wiener-Hopf operators, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), Classical Analysis and ODEs (math.CA), FOS: Mathematics, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Representation Theory (math.RT), Mathematics - Representation Theory
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