Spherical Mean
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High Quality Content by WIKIPEDIA articles! In mathematics, the spherical mean of a function around a point is the average of all values of that function on a sphere of given radius centered at that point. Consider an open set U in the Euclidean space Rn and a continuous function u defined on U with real or complex values. Let x be a point in U and r 0 be such that the closed ball B(x, r) of center x and radius r is contained in U. The spherical mean over the sphere of radius r centered at x is defined as frac{1}{omega_{n-1}(r)}intlimits_{partial B(x, r)} ! u(y) , mathrm{d} S(y) where B(x, r)…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, the spherical mean of a function around a point is the average of all values of that function on a sphere of given radius centered at that point. Consider an open set U in the Euclidean space Rn and a continuous function u defined on U with real or complex values. Let x be a point in U and r 0 be such that the closed ball B(x, r) of center x and radius r is contained in U. The spherical mean over the sphere of radius r centered at x is defined as frac{1}{omega_{n-1}(r)}intlimits_{partial B(x, r)} ! u(y) , mathrm{d} S(y) where B(x, r) is the (n 1)-sphere forming the boundary of B(x, r), dS denotes integration with respect to spherical measure and n 1(r) is the "surface area" of this (n 1)-sphere.