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 & Angkana Rüland
• E-Jahr: 2020
• Jahr: 28 Jun 2020
• Umfang: 49 S.
• Teil: volume:45
• Teil: year:2020
• Teil: number:11
• Teil: pages:1512-1560
• Teil: extent:49
• Fussnoten: Gesehen am 29.06.2021
• Titel Quelle: Enthalten in: Communications in partial differential equations
• Ort Quelle: Philadelphia, Pa. : Taylor & Francis, 1976
• Jahr Quelle: 2020
• Band/Heft Quelle: 45(2020), 11, Seite 1512-1560
• ISSN Quelle: 1532-4133
• DOI: doi:10.1080/03605302.2020.1776323
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Logarithmic stability
• Sach-SW: moment problem
• Sach-SW: nonlocal operators
• Sach-SW: unique continuation
• K10plus-PPN: 1761473263

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 Ls(D)=∑j=1n(−∂xj2)s+q with s∈[12,1) and q∈L∞ acting on functions on Rn.