A DISCREPANCY THEOREM FOR HARMONIC FUNCTIONS ON THE d DIMENSIONAL SPHERE WITH APPLICATIONS TO SCATTERINGS OF POINT CLOUDS
نویسنده
چکیده
Let d ≥ 2 be an integer, S ⊂ R the unit sphere and dσ a finite signed measure on R whose positive and negative parts are supported on S. In this paper, we derive an error estimate for the quantity ∣∣∫ Sd fdσ ∣∣, for a class of harmonic functions f : R → R. Our error estimate involves 2 sided bounds for a Newtonian potential with respect to dσ away from its support. In particular, our main result allows us to study quadrature errors, for scatterings on the sphere with given mesh norm.
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تاریخ انتشار 2006