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I am somehow puzzled by the subset $G:=L^2(I,\mathbb Z)$ of $H:=L^2(I,\mathbb R)$ of all integer valued functions on $I=[0,1]$ (in fact I mentioned as an example in this old MO question). Some simple ...

I've been reading about RKHSs and Hilbert spaces of functions these days a bit these days and I haven't yet come across an example of a hilbert space $H$ whose elements are all functions $f:\mathbb{R}^...