3 citations · 6 across the 9 of their papers we have counts for
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On the Number of Closed Gaps of Discrete Periodic One-Dimensional Operators
Andrew Arroyo, Faye Castro, Jake Fillman
From the general inverse theory of periodic Jacobi matrices, it is known that a periodic Jacobi matrix of minimal period may have at most closed spectral gaps. We…
Algebraic Properties of the Fermi Variety for Periodic Graph Operators
Jake Fillman, Wencai Liu, Rodrigo Matos
We present a method to estimate the number of irreducible components of the Fermi varieties of periodic Schrödinger operators on graphs in terms of suitable asymptotics. Our main t…
The Schwartzman Group of an Affine Transformation
David Damanik, Íris Emilsdóttir, Jake Fillman
We compute the Schwartzman group associated with an ergodic affine automorphism of a compact connected abelian group given by the composition of an automorphism of the group and a…
Discontinuities of the Integrated Density of States for Laplacians Associated with Penrose and Ammann-Beenker Tilings
David Damanik, Mark Embree, Jake Fillman +1
Aperiodic substitution tilings provide popular models for quasicrystals, materials exhibiting aperiodic order. We study the graph Laplacian associated with four tilings from the mu…
Johnson-Schwartzman Gap Labelling for Ergodic Jacobi Matrices
David Damanik, Jake Fillman, Zhenghe Zhang
We consider two-sided Jacobi matrices whose coefficients are obtained by continuous sampling along the orbits of a homeomorphim of a compact metric space. Given an ergodic probabil…
Spectra of Discrete Two-Dimensional Periodic Schrödinger Operators with Small Potentials
Mark Embree, Jake Fillman
We show that the spectrum of a discrete two-dimensional periodic Schrödinger operator on a square lattice with a sufficiently small potential is an interval, provided the period is…