Integrable operators and squares of Hankel Matrices

Details Integrable operators and squares of Hankel Matrices Integrable operators and squares of Hankel Matrices

2007-07-10

arxiv.org/abs/0707.1474v2

Mathematics

Functional Analysis

9 pages

Scientific paper

In this note, we find sufficient conditions for an operator with kernel of the form $A(x)B(y)-A(x)B(y)/(x-y)$ (which we call a Tracy-Widom type operator) to be the square of a Hankel operator. We consider two contexts: infinite matrices on $\ell^2$, and integral operators on the Hardy space $H^2(\mathbb{T})$. The results can be applied to the discrete Bessel kernel, which is significant in random matrix theory.

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