Approximation numbers = singular values
(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:
https://lup.lub.lu.se/record/687933
- author
- Bennewitz, Christer LU
- organization
- publishing date
- 2007
- 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
- 2016-04-01 17:10:58
- date last changed
- 2022-01-29 00:55:30
@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}}, keywords = {{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}}, doi = {{10.1016/j.cam.2006.10.042}}, volume = {{208}}, year = {{2007}}, }