On two methods for quantitative unique continuation results for some nonlocal operators

• Verfasst von: García-Ferrero, María Ángeles [VerfasserIn]
• Verfasst von: Rüland, Angkana [VerfasserIn]
• Titel: On two methods for quantitative unique continuation results for some nonlocal operators
• Verf.angabe: María Ángeles García-Ferrero and Angkana Rüland
• E-Jahr: 2020
• Jahr: 3 Mar 2020
• Umfang: 42 S.
• Teil: year:2020
• Teil: elocationid:2003.06402
• Teil: pages:1-42
• Teil: extent:42
• Fussnoten: Gesehen am 12.05.2021
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2020
• Band/Heft Quelle: (2020), Artikel-ID 2003.06402, Seite 1-42
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Mathematics - Analysis of PDEs
• K10plus-PPN: 1757753591

Abstract

In this article we present two mechanisms for deducing logarithmic quantitative unique continuation bounds for certain classes of integral operators. In our first method, expanding the corresponding integral kernels, we exploit the logarithmic stability of the moment problem. In our second method we rely on the presence of branch-cut singularities for certain Fourier multipliers. As an application we present quantitative Runge approximation results for the operator $ L_s(D) = \sum\limits_{j=1}^{n}(-\partial_{x_j}^2)^{s} + q$ with $s\in [\frac{1}{2},1)$ and $q\in L^{\infty}$ acting on functions on $\mathbb{R}^n$.