Open AccessOrthogonality and mean squares of the vector fields given by spherical cap harmonic potentials
Author(s) -
Lowes F. J.
Publication year - 1999
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.1999.00739.x
Subject(s) - spherical harmonics , vector spherical harmonics , orthogonality , harmonics , mathematical analysis , spin weighted spherical harmonics , mathematics , harmonic , zonal spherical harmonics , least squares function approximation , physics , geometry , acoustics , quantum mechanics , statistics , estimator , voltage
It is well known that the vector fields derived from spherical harmonics are orthogonal over the sphere. It is now shown that the vector fields derived from spherical cap harmonics are orthogonal over the cap, to the same extent as the cap potentials are, and expressions are given for their mean squares.