Abstract
In this paper, we define time-independent modifiers to construct a long-range scattering theory for a class of difference operators on \(\mathbb {Z}^d\), including the discrete Schrödinger operators on the square lattice. The modifiers are constructed by observing the corresponding Hamilton flow on \(T^*\mathbb {T}^d\). We prove the existence and completeness of modified wave operators in terms of the above-mentioned time-independent modifiers.
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Acknowledgements
The author would like to thank Professor Shu Nakamura, my Ph.D. advisor. This paper would not be completed without his advice. The author is also grateful to Professor Hiroshi Isozaki for his kind discussion.
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Communicated by Jan Derezinski.
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Tadano, Y. Long-Range Scattering for Discrete Schrödinger Operators. Ann. Henri Poincaré 20, 1439–1469 (2019). https://doi.org/10.1007/s00023-019-00763-w
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DOI: https://doi.org/10.1007/s00023-019-00763-w