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The Fredholm index of locally compact band-dominated operators on $L^p (R)$

Vladimir S. Rabinovich·Steffen Roch
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Abstract

We establish a necessary and sufficient criterion for the Fredholmness of a general locally compact band-dominated operator $A$ on $L^p(R)$ 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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Vladimir S. Rabinovich, Steffen Roch. 2006-04-06. The Fredholm index of locally compact band-dominated operators on $L^p (R)$. https://arxiv.org/abs/math/0604128

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