Integrable operators and the squares of Hankel operators

Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distributions of large self-adjoint random matrices from the generalized unitary ensembles. This paper gives sufficient conditions for an integrable operator to be the square of a Hankel operator, and applies the condition to the Airy, associated Laguerre, modified Besses and Whittaker functions.