Finite section method for aperiodic Schrödinger operators
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We consider discrete Schrödinger operators with aperiodic potentials given by a Sturmian word, which is a natural generalisation of the Fibonacci-Hamiltonian. We introduce the finite section method, which is often used to solve operator equations approximately, and apply it first to periodic Schrödinger operators. It turns out that the applicability of the method is always guaranteed for integer-valued potentials. By using periodic approximations, we find a necessary and sufficient condition for the applicability of the finite section method for aperiodic Schrödinger operators and a numerical method to check it.
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