I agree with @lindahua, this is actually a linear operator acting on a vector space of indeterminate dimension. In principle there is no reason why you could not multiply this with a matrix or vector that is nominally infinite-dimensional, such as those provided by [ApproxFun.jl](https://github.com/dlfivefifty/ApproxFun)

`cumsum` and `fft` are also classic examples of linear operators.