= Contraction generator from an exponentially weighted difference operator
{title2=$(Qf)_0=-f_0,\quad (Qf)_n=4^n(f_{n-1}/2-f_n)$}
On its maximal domain in $\ell^2$, put $g_n=2^nf_n$. Then $g_n-g_{n-1}=-2^{-n}(Qf)_n$, so $g_n$ has a finite limit $\ell_f$. Summation gives $\operatorname{Re}\langle Qf,f\rangle=-\tfrac12(|g_0|^2+|\ell_f|^2+\sum_{n\geq1}|g_n-g_{n-1}|^2)$. For $\alpha>0$, the resolvent equation is the recursion $g_n=(g_{n-1}+2^{-n}h_n)/(1+\alpha4^{-n})$, which produces a bounded $g_n$ and hence $f\in\ell^2$. The <Lumer-Phillips theorem> proves contraction-semigroup generation.
// Target: analysis.bigb
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