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## Hankel operators that commute with second order differential operators.

Research output: Contribution to journalJournal article

Published
Journal publication date 1/06/2008 Journal of Mathematical Analysis and Applications 1 342 14 601-614 Published English

### 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.

### Bibliographic note

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.