2020/03/13 by María Ángeles García‐Ferrero, García-Ferrero, María Ángeles, Angkana Rüland +1
Mathematics · #Analysis of PDEs (math.AP) #Analytic continuation #Applied mathematics #Computer science #Continuation #Differential Equations and Boundary Problems #FOS: Mathematics #Fourier transform #Gravitational singularity #Logarithm #Mathematical analysis #Mathematics #Moment (physics) #Numerical methods in inverse problems #Operator (biology) #Physics #Pure mathematics #Quantum mechanics #Spectral Theory in Mathematical Physics #Stability (learning theory)
paper · pdf · doi:10.48550/arxiv.2003.06402
openalex publication_date 2020/03/13 · openalex created_date 2022/07/26 · openalex updated_date 2026/08/05
In this article we present two mechanisms for deducing logarithmic\nquantitative unique continuation bounds for certain classes of integral\noperators. In our first method, expanding the corresponding integral kernels,\nwe exploit the logarithmic stability of the moment problem. In our second\nmethod we rely on the presence of branch-cut singularities for certain Fourier\nmultipliers. As an application we present quantitative Runge approximation\nresults for the operator Ls(D) =\n\∑\j=1n(-\∂xj2)s + q with s\∈ [\(1)/(2),1)\nand q\∈ L\∞ acting on functions on \ℝn.\n