Advanced

Approximation numbers = singular values

Bennewitz, Christer LU (2007) In Journal of Computational and Applied Mathematics 208(1). p.102-110
Abstract
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. (c) 2006 Published by Elsevier B.V.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Pruefer transform, eigenvalue, generalised trigonometric function, asymptotics, Bernstein width, Sturm-Liouville
in
Journal of Computational and Applied Mathematics
volume
208
issue
1
pages
102 - 110
publisher
Elsevier
external identifiers
  • wos:000249311300008
  • scopus:34547588520
ISSN
0377-0427
DOI
10.1016/j.cam.2006.10.042
language
English
LU publication?
yes
id
633309e8-2bc6-40be-8b9b-24ae06bedb01 (old id 687933)
date added to LUP
2007-12-07 15:52:54
date last changed
2017-10-01 04:53:45
@article{633309e8-2bc6-40be-8b9b-24ae06bedb01,
  abstract     = {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. (c) 2006 Published by Elsevier B.V.},
  author       = {Bennewitz, Christer},
  issn         = {0377-0427},
  keyword      = {Pruefer transform,eigenvalue,generalised trigonometric function,asymptotics,Bernstein width,Sturm-Liouville},
  language     = {eng},
  number       = {1},
  pages        = {102--110},
  publisher    = {Elsevier},
  series       = {Journal of Computational and Applied Mathematics},
  title        = {Approximation numbers = singular values},
  url          = {http://dx.doi.org/10.1016/j.cam.2006.10.042},
  volume       = {208},
  year         = {2007},
}