Abstract
From the theory of Fourier series on the unit circle we know that when n = 2, every f ∈ L 2(S) has an expansion of the form
where the sum converges in L 2(S). In this chapter we will see that an analogous expansion is valid for functions f ∈ L 2(S) when n > 2, with objects known as spherical harmonics playing the roles of the exponentials e imθ.
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© 1992 Springer Science+Business Media New York
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Axler, S., Bourdon, P., Ramey, W. (1992). Spherical Harmonics. In: Harmonic Function Theory. Graduate Texts in Mathematics, vol 137. Springer, New York, NY. https://doi.org/10.1007/0-387-21527-1_5
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DOI: https://doi.org/10.1007/0-387-21527-1_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4899-1186-5
Online ISBN: 978-0-387-21527-3
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