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Multidimensional Almost-Periodic Schrödinger Operators with Cantor Spectrum
David Damanik, Jake Fillman, Anton Gorodetski
We construct multidimensional almost-periodic Schrödinger operators whose spectrum has zero lower box counting dimension. In particular, the spectrum in these cases is a generalize…
Discrete Bethe--Sommerfeld Conjecture for Triangular, Square, and Hexagonal Lattices
Jake Fillman, Rui Han
We study discrete Schrödinger operators on the graphs corresponding to the triangular lattice, the hexagonal lattice, and the square lattice with next-nearest neighbor interactions…
Spectral Properties of Limit-Periodic Operators
David Damanik, Jake Fillman
We survey results concerning the spectral properties of limit-periodic operators. The main focus is on discrete one-dimensional Schrödinger operators, but other classes of operator…
Limit-Periodic Schrödinger Operators With Lipschitz Continuous IDS
David Damanik, Jake Fillman
We show that there exist limit-periodic Schrödinger operators such that the associated integrated density of states is Lipschitz continuous. These operators arise in the inverse sp…