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
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: | Journal 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: | ?? qa ?? |
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: | 14 Apr 2018 00:10 |
Identification Number: | |
URI: | http://eprints.lancs.ac.uk/id/eprint/843 |
---|
Actions (login required)