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The problem of obtaining a representation of a variable on a sphere from irregularly distributed observations is divided into two topics (1) Spectral representation: the relationships between covariances, spherical harmonic coefficients, power spectra, etc.; and (2) statistical analysis: extrapolation, power spectrum, and coefficient determination, etc., under the assumption of stationarity. The relationships of various techniques are discussed.
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W. M. Kaula (1967) studied this question.
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