, Volume 57, Issue 2, pp 263-281
Date: 08 Aug 2006

The Fredholm Index of Locally Compact Band-dominated Operators on \(L^p \,(\user2{\mathbb{R}})\)

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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.