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 we...
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| Main Authors: | , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
3 Mar 2020
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| In: |
Arxiv
Year: 2020, Pages: 1-42 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2003.06402
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| Author Notes: | María Ángeles García-Ferrero and 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 $ 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 $\mathbb{R}^n$. |
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| Item Description: | Gesehen am 12.05.2021 |
| Physical Description: | Online Resource |