Integrable operators and squares of Hankel operators.

Blower, Gordon (2008) Integrable operators and squares of Hankel operators. Journal of Mathematical Analysis and Applications, 340 (2). pp. 943-953. ISSN 0022-247X

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Abstract

Integrable operators arise in random matrix teory, where they describe the asymptotic 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 Bessel and Whittaker functions.