Approximation values

✍ Scribed by Christer Bennewitz

• Book ID: 104005299
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 170 KB
• Volume: 208
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2006.10.042

✦ Synopsis

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.