Exponential instability in the fractional Calderón problem
In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'o...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Dokumenttyp: | Article (Journal) Kapitel/Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
13 Nov 2017
|
| In: |
Arxiv
Year: 2017, Pages: 1-17 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1711.04799
|
| Verfasserangaben: | Angkana Rüland and Mikko Salo |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1758195290 | ||
| 003 | DE-627 | ||
| 005 | 20220819212138.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 210519s2017 xx |||||o 00| ||eng c | ||
| 035 | |a (DE-627)1758195290 | ||
| 035 | |a (DE-599)KXP1758195290 | ||
| 035 | |a (OCoLC)1341413701 | ||
| 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 13 Nov 2017 | |
| 300 | |a 17 | ||
| 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 note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on 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 \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on problem and the truncated Hilbert transform. | ||
| 650 | 4 | |a Mathematics - Analysis of PDEs | |
| 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 Arxiv |d Ithaca, NY : Cornell University, 1991 |g (2017), Artikel-ID 1711.04799, Seite 1-17 |h Online-Ressource |w (DE-627)509006531 |w (DE-600)2225896-6 |w (DE-576)28130436X |7 nnas |a Exponential instability in the fractional Calderón problem |
| 773 | 1 | 8 | |g year:2017 |g elocationid:1711.04799 |g pages:1-17 |g extent:17 |a Exponential instability in the fractional Calderón problem |
| 856 | 4 | 0 | |u http://arxiv.org/abs/1711.04799 |x Verlag |z lizenzpflichtig |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20210519 | ||
| 993 | |a Article | ||
| 994 | |a 2017 | ||
| 998 | |g 1051987679 |a Rüland, Angkana |m 1051987679:Rüland, Angkana |p 1 |x j | ||
| 999 | |a KXP-PPN1758195290 |e 392975312X | ||
| BIB | |a Y | ||
| JSO | |a {"language":["eng"],"recId":"1758195290","note":["Gesehen am 19.05.2021"],"type":{"bibl":"chapter","media":"Online-Ressource"},"title":[{"title_sort":"Exponential instability in the fractional Calderón problem","title":"Exponential instability in the fractional Calderón problem"}],"person":[{"family":"Rüland","given":"Angkana","display":"Rüland, Angkana","roleDisplay":"VerfasserIn","role":"aut"},{"role":"aut","display":"Salo, Mikko","roleDisplay":"VerfasserIn","given":"Mikko","family":"Salo"}],"relHost":[{"disp":"Exponential instability in the fractional Calderón problemArxiv","note":["Gesehen am 28.05.2024"],"type":{"media":"Online-Ressource","bibl":"edited-book"},"recId":"509006531","language":["eng"],"pubHistory":["1991 -"],"titleAlt":[{"title":"Arxiv.org"},{"title":"Arxiv.org e-print archive"},{"title":"Arxiv e-print archive"},{"title":"De.arxiv.org"}],"part":{"extent":"17","text":"(2017), Artikel-ID 1711.04799, Seite 1-17","pages":"1-17","year":"2017"},"title":[{"title":"Arxiv","title_sort":"Arxiv"}],"physDesc":[{"extent":"Online-Ressource"}],"origin":[{"publisherPlace":"Ithaca, NY ; [Erscheinungsort nicht ermittelbar]","dateIssuedDisp":"1991-","dateIssuedKey":"1991","publisher":"Cornell University ; Arxiv.org"}],"id":{"zdb":["2225896-6"],"eki":["509006531"]}}],"physDesc":[{"extent":"17 S."}],"id":{"eki":["1758195290"]},"origin":[{"dateIssuedDisp":"13 Nov 2017","dateIssuedKey":"2017"}],"name":{"displayForm":["Angkana Rüland and Mikko Salo"]}} | ||
| SRT | |a RUELANDANGEXPONENTIA1320 | ||