Abstract.
We establish a necessary and sufficient criterion for the Fredholmness of a general locally compact band-dominated operator A on \(L^p \,(\user2{\mathbb{R}})\) and solve the long-standing problem of computing its Fredholm index in terms of the limit operators of A. The results are applied to operators of convolution type with almost periodic symbol.
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Rabinovich, V.S., Roch, S. The Fredholm Index of Locally Compact Band-dominated Operators on \(L^p \,(\user2{\mathbb{R}})\). Integr. equ. oper. theory 57, 263–281 (2007). https://doi.org/10.1007/s00020-006-1456-y
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DOI: https://doi.org/10.1007/s00020-006-1456-y