Sheehan Olver

I've started the package here https://github.com/JuliaApproximation/InfiniteArrays.jl `1:∞` works pretty well, I think this is going to be a fun project. When this change takes place, ApproxFun will almost consist of...

This is implemented now in development (0.6 only)

> Another extension would be an array whose entries are defined by a function, which would be truly infinite-dimensional! I was thinking about doing brown Ian motion this way, where...

ProductFun, sure. LowRankFun, probably not: its not linear

Also, ProductFun is different then storing in a `Matrix`. a `Matrix` won't work because even if the coefficients are an `Array`, they are treated like a `Vector` for padding.

Yes. But then the current implementation would have to be changed.

The issue is with the padding. But I think what we want is to move that to the coefficient storage type. And depending on the order you want the coefficients...

Your data appears to be on an evenly spaced grid, where `transform` uses a Chebyshev grid. See https://juliaapproximation.github.io/ApproxFun.jl/latest/faq/ for an explanation of how to do least squares at an evenly...

Splines are implemented in ContinuumArrays.jl which is a future backend for ApproxFun see also CompactBases.jl for more sophisticated examples

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