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Julia package for function approximation

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Can ApproxFun.jl compute the inner product between two functions in a Hilbert space? https://discourse.julialang.org/t/packages-defining-functional-data-types/73539

First of all, thank you for developing this package, it's a very instructive way to learn about function decomposition methods! And I do like the way time dependent PDEs can...

Since differential programming is all the rage in Julia, do you think it will one day be possible to use nonlinear optimization packages where objective functions include ApproxFun `Fun`s? [Here](https://github.com/mjyshin/math-tutorials/blob/main/parameter_estimation.ipynb)...

For some reason, calling `Circle()` in REPL displays the three o'clock symbol: ```julia-repl julia> VERSION v"1.7.2-pre.0" (@v1.7) pkg> st ApproxFun Status `~/.julia/environments/v1.7/Project.toml` [28f2ccd6] ApproxFun v0.13.0 julia> using ApproxFun julia> Circle()...

Broadcasting a function fails on a product space: ```julia-repl (@v1.8) pkg> st ApproxFun Status `~/.julia/environments/v1.8/Project.toml` [28f2ccd6] ApproxFun v0.13.0 julia> d = Domain(-1..1)^2; julia> x,y = Fun(d); julia> exp.(x) ERROR: MethodError:...

I find that evaluating `Fun` defined on a product space with integer coefficients generates an error: ```julia-repl julia> VERSION v"1.7.2-pre.0" (@v1.7) pkg> st ApproxFun Status `~/.julia/environments/v1.7/Project.toml` [28f2ccd6] ApproxFun v0.13.0 julia>...

[This section](https://juliaapproximation.github.io/ApproxFun.jl/stable/usage/equations/#Partial-differential-equations-1) of the documentation says `# Δ is an alias for Laplacian()`, but it is not exported: ```julia-repl (@v1.8) pkg> st ApproxFun Status `~/.julia/environments/v1.8/Project.toml` [28f2ccd6] ApproxFun v0.13.0 julia> Δ...

The code seems to be creating errors by trying to evaluate at endpoints of an open interval, when the function might not exist at these endpoints: ``` julia> d (0.0..3.0...

The attached code shows two cases of attempting to solve an ODE problem using ApproxFun. Changing the interval endpoint, without any other code changes, results in a shift from successful...

I try to solve the following nonlinear Differential Equation/Boundary Value Problem: y'''' + 4.0*y'''/x = 0 with the following boundary conditions y(0) = y'(0) = 0 y''(1)=0 y'''(1)=1 in a...