Exponential instability in the fractional Calderón problem
In this paper we prove the exponential instability of the fractional Calderón problem and thus prove the optimality of the logarithmic stability estimate from Rüland and Salo (2017 arXiv:1708.06294). In order to infer this result, we follow the strategy introduced by Mandache in (2001 Inverse Prob...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
20 February 2018
|
| In: |
Inverse problems
Year: 2018, Jahrgang: 34, Heft: 4, Pages: 1-21 |
| ISSN: | 1361-6420 |
| DOI: | 10.1088/1361-6420/aaac5a |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1088/1361-6420/aaac5a
|
| Verfasserangaben: | Angkana Rüland and Mikko Salo |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1758194707 | ||
| 003 | DE-627 | ||
| 005 | 20220819212127.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 210519s2018 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1088/1361-6420/aaac5a |2 doi | |
| 035 | |a (DE-627)1758194707 | ||
| 035 | |a (DE-599)KXP1758194707 | ||
| 035 | |a (OCoLC)1341413700 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Rüland, Angkana |d 1987- |e VerfasserIn |0 (DE-588)1051987679 |0 (DE-627)787342378 |0 (DE-576)407655506 |4 aut | |
| 245 | 1 | 0 | |a Exponential instability in the fractional Calderón problem |c Angkana Rüland and Mikko Salo |
| 264 | 1 | |c 20 February 2018 | |
| 300 | |a 21 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Gesehen am 19.05.2021 | ||
| 520 | |a In this paper we prove the exponential instability of the fractional Calderón problem and thus prove the optimality of the logarithmic stability estimate from Rüland and Salo (2017 arXiv:1708.06294). In order to infer this result, we follow the strategy introduced by Mandache in (2001 Inverse Problems 17 1435) for the standard Calderón problem. Here we exploit a close relation between the fractional Calderón problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in Rüland and Salo (2017 arXiv:1708.06294). Finally, in one dimension, we show a close relation between the fractional Calderón problem and the truncated Hilbert transform. | ||
| 700 | 1 | |a Salo, Mikko |d 1979- |e VerfasserIn |0 (DE-588)173729959 |0 (DE-627)698635841 |0 (DE-576)134570995 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Inverse problems |d Bristol [u.a.] : Inst., 1985 |g 34(2018), 4, Artikel-ID 045003, Seite 1-21 |h Online-Ressource |w (DE-627)270426108 |w (DE-600)1477292-9 |w (DE-576)078189306 |x 1361-6420 |7 nnas |a Exponential instability in the fractional Calderón problem |
| 773 | 1 | 8 | |g volume:34 |g year:2018 |g number:4 |g elocationid:045003 |g pages:1-21 |g extent:21 |a Exponential instability in the fractional Calderón problem |
| 856 | 4 | 0 | |u https://doi.org/10.1088/1361-6420/aaac5a |x Verlag |x Resolving-System |z lizenzpflichtig |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20210519 | ||
| 993 | |a Article | ||
| 994 | |a 2018 | ||
| 998 | |g 1051987679 |a Rüland, Angkana |m 1051987679:Rüland, Angkana |p 1 |x j | ||
| 999 | |a KXP-PPN1758194707 |e 392975214X | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"note":["Gesehen am 19.05.2021"],"type":{"bibl":"article-journal","media":"Online-Ressource"},"language":["eng"],"recId":"1758194707","title":[{"title_sort":"Exponential instability in the fractional Calderón problem","title":"Exponential instability in the fractional Calderón problem"}],"person":[{"display":"Rüland, Angkana","roleDisplay":"VerfasserIn","role":"aut","family":"Rüland","given":"Angkana"},{"roleDisplay":"VerfasserIn","display":"Salo, Mikko","role":"aut","family":"Salo","given":"Mikko"}],"physDesc":[{"extent":"21 S."}],"relHost":[{"pubHistory":["1.1985 -"],"titleAlt":[{"title":"an international journal of inverse problems, inverse methods and computerized inversion of data"},{"title":"a journal recognized by the European Physical Society"}],"part":{"volume":"34","text":"34(2018), 4, Artikel-ID 045003, Seite 1-21","extent":"21","year":"2018","issue":"4","pages":"1-21"},"disp":"Exponential instability in the fractional Calderón problemInverse problems","note":["Gesehen am 21.09.2020"],"type":{"media":"Online-Ressource","bibl":"periodical"},"language":["eng"],"recId":"270426108","title":[{"title":"Inverse problems","subtitle":"an international journal on the theory and practice of inverse problems, inverse methods and computerized inversion of data","title_sort":"Inverse problems"}],"physDesc":[{"extent":"Online-Ressource"}],"origin":[{"publisherPlace":"Bristol [u.a.]","publisher":"Inst.","dateIssuedKey":"1985","dateIssuedDisp":"1985-"}],"id":{"eki":["270426108"],"zdb":["1477292-9"],"issn":["1361-6420"]},"name":{"displayForm":["Institute of Physics, London and Bristol"]}}],"origin":[{"dateIssuedDisp":"20 February 2018","dateIssuedKey":"2018"}],"id":{"doi":["10.1088/1361-6420/aaac5a"],"eki":["1758194707"]},"name":{"displayForm":["Angkana Rüland and Mikko Salo"]}} | ||
| SRT | |a RUELANDANGEXPONENTIA2020 | ||