Any package out there defining a function type with inner product? In functional data analysis we often define the inner product between two functions as
\langle f, g \rangle = \int_a^b f(t)\bar{g(t)} dt
More formally, this defines the Hilbert space of functions in the interval [a,b].
I used to write some simple implementations for functional data analysis mimicking what the R package fda does. To my knowledge, there is no Julia package dedicated for FDA, and my quick and dirty suggestion (and what I have been doing) is to evaluate the two functions at discrete points and approximate the inner product of two functions with vector inner product.
ApproxFun.jl has useful definitions, it is just not exposed to end users yet:
https://github.com/JuliaApproximation/ApproxFun.jl/issues/753