Integrable operators and the squares of Hankel operators

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

Abstract

Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution 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.