General: If $f \in C^1$ is a periodic function defined over some multi-dimensional space, then it should be possible to express $f$ as a FINITE fourier series.
- is this true of any periodic basis?
- is there a way to determine the number of terms in this finite series?
Specific: I have a function that is smooth and continuous and is defined on the unit hypersphere. I want to know:
- is it possible to represent this function as a FINITE series in the hyperspherical harmonic basis?
- how many terms will it take?