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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 or Publication Title: Journal of Mathematical Analysis and Applications
    Additional Information: 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.
    Uncontrolled Keywords: random matrices ; Tracy--Widom operators
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 843
    Deposited By: Professor Gordon Blower
    Deposited On: 13 Dec 2007 13:16
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 13:14
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/843

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