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In this note, we find sufficient conditions for an operator with kernel ofthe 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: infinitematrices 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.

Integrable operators and squares of Hankel Matrices