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Hankel operators that commute with second order differential operators.

Research output: Contribution to journalJournal article

Published

Journal publication date1/06/2008
JournalJournal of Mathematical Analysis and Applications
Journal number1
Volume342
Number of pages14
Pages601-614
Original languageEnglish

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.