Let's say I have the Spherical harmonic series decomposition of a tensor with given series coefficients, and it is equal to another spherical harmonic series decomposition with unknown coefficients. Are the series coefficients necessarily equal? What is their relation if not?
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I feel like it could only vary up to a phase factor in the harmonics pulled into the coefficient? – Ryan Rankin Jul 20 '15 at 22:46
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Orthogonality relations should reveal the relation? – Ryan Rankin Jul 20 '15 at 22:47
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What is the difference of the tensors? What are its coefficients? – Travis Willse Jul 20 '15 at 22:51