Topological Content of the Maxwell Theorem on Multipole Representation of Spherical Functions
نویسنده
چکیده
Theorem 1. The nth derivative of the function 1/r along n constant (translation-invariant) vector fields in R coincides on the sphere with a spherical function of degree n. Any nonzero spherical function of degree n can be obtained by this construction from some n-tuple of nonzero vector fields. These n fields are uniquely defined by the function (up to multiplication by nonzero constants and permutation of the n fields).
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