TY - JOUR

T1 - Hankel operators that commute with second order differential operators.

AU - Blower, Gordon

N1 - 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.

PY - 2008/6/1

Y1 - 2008/6/1

N2 - 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.

AB - 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.

KW - random matrices

KW - Tracy--Widom operators

U2 - 10.1016/j.jmaa.2007.12.028

DO - 10.1016/j.jmaa.2007.12.028

M3 - Journal article

VL - 342

SP - 601

EP - 614

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -