In the L^2-based metric completion induced by the BBM candidate metric, the BBM eigenfunctions are absent and the free transported Hamiltonian is the dilation generator with purely absolutely continuous spectrum.
Connes,Trace formula in noncommutative geometry and the zeros of the Riemann zeta function, Selecta Math
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Metric completion of the Bender--Brody--M\"uller Hamiltonian: dilation spectrum and missing eigenstates
In the L^2-based metric completion induced by the BBM candidate metric, the BBM eigenfunctions are absent and the free transported Hamiltonian is the dilation generator with purely absolutely continuous spectrum.