# Hankel operators that commute with second order differential operators.

Blower, Gordon (2008) Hankel operators that commute with second order differential operators. Journal of Mathematical Analysis and Applications, 342 (1). pp. 601-614. ISSN 0022-247X

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## Abstract

Suppose that $\Gamma$ is a continuous and self-adjoint Hankel operator on $L^2(0, \infty )$ with kernel $\phi (x+y)$ and that $Lf=-(d/dx)(a(x)df/dx)+b(x)f(x) with$a(0)=0$. If$a$and$b$are both quadratic, hyperbolic or trigonometric functions, and$\phi$satisfies a suitable form of Gauss's hypergeometric differential equation, or the confluent hypergeometric equation, then$\Gamma L=L\Gamma\$. There are also results proving rapid decay of the singular numbers of Hankel integral operators with kernels that are analytic and of exponential decay in the right half-plane.

Item Type: Article Journal of Mathematical Analysis and Applications MSC20000 47B35 The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 342 (1), 2008, © ELSEVIER. random matrices ; Tracy--Widom operators Q Science > QA Mathematics Faculty of Science and Technology > Mathematics and Statistics 843 Professor Gordon Blower 13 Dec 2007 13:16 Yes Published 09 Oct 2013 13:14 http://eprints.lancs.ac.uk/id/eprint/843