Abstract:Differential operators commuting with integral operators were discovered in the work of C. Tracy and H. Widom [37,38] and used to derive asymptotic expansions of the Fredholm determinants of integral operators arising in random matrix theory. Very recently, it has been proved that all rational, symmetric Darboux transformations of the Bessel, Airy, and exponential bispectral functions give rise to commuting integral and differential operators [6,7,8], vastly generalizing the known examples in the literature. I… Show more
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