New results on the degree of ill-posedness for integration operators with weights

Description

We extend our results on the degree of ill-posedness for linear integration opera-
tors A with weights mapping in the Hilbert space L^2(0,1), which were published in
the journal 'Inverse Problems' in 2005 ([5]). Now we can prove that the degree one
also holds for a family of exponential weight functions. In this context, we empha-
size that for integration operators with outer weights the use of the operator AA^*
is more appropriate for the analysis of eigenvalue problems and the corresponding
asymptotics of singular values than the former use of A^*A.

Links & Downloads

1. urn:nbn:de:bsz:ch1-200800545
2. https://monarch.qucosa.de/id/qucosa%3A18900
3. https://monarch.qucosa.de/api/qucosa%3A18900/attachment/ATT-0/
4. https://monarch.qucosa.de/api/qucosa%3A18900/attachment/ATT-1/

Tags

info:eu-repo/classification/ddc/510

ddc:510

Eigenwertproblem

Inverses Problem

Bessel function

Compact integral operator

Degree of ill-posedness

Singular value asymptotics

Additional Fields

Identifer	oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18900
Date	16 May 2008
Creators	Hofmann, Bernd, von Wolfersdorf, Lothar
Publisher	Technische Universität Chemnitz
Source Sets	Hochschulschriftenserver (HSSS) der SLUB Dresden
Language	English
Detected Language	English
Type	doc-type:conferenceObject, info:eu-repo/semantics/conferenceObject, doc-type:Text
Rights	info:eu-repo/semantics/openAccess
Relation	urn:nbn:de:bsz:ch1-200800505, qucosa:18897