Discoveries / analysis

The Graveyard Problem for Dissipative Barrier Truncations

The dissipative barrier method suppresses spectral pollution when a differential operator is truncated, but can it hide genuine spectral points? Known as the graveyard problem, the question stayed open in dimension two and above for more than a decade. It cannot: for Schrodinger operators in dimensions $d \ge 2$ no spectral point becomes invisible, which together with the known one-dimensional theorem settles no-invisibility in every dimension.