2
votes
0answers
81 views

expansion of function on spherical harmonics

Let $f :S^{n-1}\longrightarrow R_+$ be a square integrable function. Let $\{Y_{j,k}\}$ be an orthonormal basis of spherical harmonics on $S^{n-1}$, $j\in Z_+$ and $k=1, \ldots, d_n(j)$, where $d_n(j)$ ...
1
vote
1answer
83 views

Question which involves Riesz potential

Let $f :S^{n-1}\longrightarrow R_+$ , $P_{j,k}. j,k \in N$ be a spherical harmonics (http://en.wikipedia.org/wiki/Spherical_harmonics) and $\displaystyle{f\left(\frac{x}{|x|}\right)|x|^{1-\frac ...
3
votes
0answers
567 views

Fourier Transform of spherical harmonics

I am trying seeking for definition (or some source) of the Fourier Transform of Spherical Harmonics (see https://en.wikipedia.org/wiki/Spherical_harmonics). Any help will be really appreciated. ...