I hope you are well.
Could you help me with the following?
I want to build a set of quasi-periodic functions that are also orthonormal. This set will help me with a chaos problem. I tried with $\sin (\sqrt (2) x) + \sin (x)$ style functions and using inner product $< f(x),g(x) > = \int_{- \pi}^{\pi} f(x) \cdot g(x) dx =0$. I may be overlooking things so if you could recommend literature that includes definitions and basic properties of quasi-periodic functions, almost-periodic functions.
Thank you all.