2017/08/14 by Angkana Rüland, Rüland, Angkana
Mathematics · #Numerical methods in inverse problems #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1708.04285
In this article we derive quantitative uniqueness and approximation\nproperties for (perturbations) of Riesz transforms. Seeking to provide robust\narguments, we adopt a PDE point of view and realize our operators as harmonic\nextensions, which makes the problem accessible to PDE tools. In this context we\nthen invoke quantitative propagation of smallness estimates in combination with\nqualitative Runge approximation results. These results can be viewed as\nquantifications of the approximation properties which have recently gained\nprominence in the context of nonlocal operators, c.f. [DSV14], [DSV16].\n