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Focusing on the multidimensional Schrödinger operator with a periodic potential, this book tackles both direct and inverse problems, emphasizing perturbation theory and the determination of spectral invariants. It presents a novel method for deriving asymptotic formulas for Bloch eigenvalues and functions in any dimension. The text constructs and estimates iso-energetic surfaces in high energy regions, supporting the Bethe-Sommerfeld conjecture. Additionally, it provides an algorithm for uniquely determining the potential using Bloch eigenvalues as input data.
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Multidimensional Periodic Schrödinger Operator, Oktay Veliev
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- 2016
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