Tagged Questions
1
vote
0answers
28 views
Variation on a completeness relation
The completeness relation for the spherical harmonics is:
$$\sum_{l=0}^{\infty} \sum_{m=-l}^{l} Y_{lm}^*\left(\theta_1,\phi_1\right)Y_{lm}\left(\theta_2,\phi_2\right) = ...
0
votes
0answers
55 views
Show that function is a constant
Let $\phi \in L^2(S^{n})$. Let $f=\phi^2$ and let $f_j^m$ be a Fourier coefficients of $f$.
Help me please to show that if
$$
\sum_{j,i}c_jf^m_jY^i_j=\phi,
$$
then $f=constant$.
Here $Y_j^i$ is the ...
2
votes
0answers
324 views
Spherical harmonics give all the irreducible representations of $SO(3)$?
It is mentioned in Wiki that the spaces $\mathcal{H}_{k}$ of spherical harmonics of degree $k$ give ALL the irreducible representations of $SO(3)$. Could anyone tell me where can I find the proof? ...
