Boundary terms exclude formal adjoint eigenvectors

The formal adjoint of an infinite matrix does not specify the domain of the true adjoint. For the weighted difference generator $(Qf{)}_n=4^n(f_{n-1}/2-f_n)$, its formal positive-eigenvalue solution is $h_n=2^{-n}{h}_0{\prod }_{k<n}(1+\alpha 4^{-k})$. This is square summable but does not belong to the true adjoint domain of the maximal operator: testing against $f_n=2^{-n}$ contradicts the adjoint identity. The nonzero limiting boundary term is the obstruction.

// Target: analysis.bigb