Open AccessA Completeness Theorem for Expansions of a Vector Function in Spherical Harmonics
Author(s) -
Jeffreys Sir Harold
Publication year - 1967
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1967.tb03126.x
Subject(s) - spherical harmonics , vector spherical harmonics , mathematics , completeness (order theory) , spheres , mathematical analysis , notation , vector valued function , set (abstract data type) , spin weighted spherical harmonics , fuzzy sphere , harmonics , pure mathematics , physics , computer science , arithmetic , quantum mechanics , astronomy , voltage , programming language
Summary A proof is given that the F, G, H notation is adequate for expressing a vector function in a sphere in terms of spherical harmonics, subject to convergence conditions; that is, the terms are linearly independent (and can in fact be made orthogonal) and form a complete set such that no non‐zero set of components expansible over spheres can be orthogonal to all of them.