On two methods for quantitative unique continuation results for some nonlocal operators
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 w...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
28 Jun 2020
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| In: |
Communications in partial differential equations
Year: 2020, Volume: 45, Issue: 11, Pages: 1512-1560 |
| ISSN: | 1532-4133 |
| DOI: | 10.1080/03605302.2020.1776323 |
| Online Access: | Resolving-System, lizenzpflichtig, Volltext: https://doi.org/10.1080/03605302.2020.1776323 Verlag, lizenzpflichtig, Volltext: https://www.tandfonline.com/doi/full/10.1080/03605302.2020.1776323 
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| Author Notes: | María Ángeles García-Ferrero & Angkana Rüland |
| Summary: | 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. |
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| Item Description: | Gesehen am 29.06.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1532-4133 |
| DOI: | 10.1080/03605302.2020.1776323 |