Approximation numbers=singular values
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摘要
This paper introduces a generalisation of the notion of singular value for Hilbert space operators to more general Banach spaces. It is shown that for a simple integral operator of Hardy type the singular values are the eigenvalues of a non-linear Sturm-Liouville equation and coincide with the approximation numbers of the operator. Finally, asymptotic formulas for the singular numbers are deduced.
论文关键词：34B15,34B24,34L20,34L30,Sturm-Liouville,Bernstein width,Pruefer transform,Eigenvalue asymptotics,Generalised trigonometric function
论文评审过程：Received 28 July 2005, Available online 6 December 2006.
论文官网地址：https://doi.org/10.1016/j.cam.2006.10.042
