Here is my question: A basic result of classical Fourier analysis is that the fourier coefficients of an $L^1$ function must tend to zero (Riemann-Lebesgue Lemma). Is there analogous result to the spherical harmonic expansions? And how can we prove it ?
It will be great if someone can help me here or/and can also provide few good references for the same.
ps: 1) I also found this question in a text book: [Geometric Analysis of the Bergman Kernel and Metric][1]from where I reformulated my question.
2) I am not a mathematician so please bear my naive comments in discussions.