Finite sections of the Fibonacci Hamiltonian
arXiv:1711.098483 citationsh-index: 15
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Provides a rigorous stability result for truncations of aperiodic Schrödinger operators, relevant to mathematical physics and numerical analysis.
The paper proves that finite principal submatrices of the infinite Fibonacci Hamiltonian are always stable, meaning they are invertible for large n and their inverses converge pointwise to the inverse of the infinite operator.
We study finite but growing principal square submatrices $A_n$ of the one- or two-sided infinite Fibonacci Hamiltonian $A$. Our results show that such a sequence $(A_n)$, no matter how the points of truncation are chosen, is always stable -- implying that $A_n$ is invertible for sufficiently large $n$ and $A_n^{-1}\to A^{-1}$ pointwise.