Integral Equations and Operator Theory

, Volume 57, Issue 2, pp 263–281 | Cite as

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

Article

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.

Mathematics Subject Classification (2000).

Primary 47A53 Secondary 47G10 45E10 

Keywords.

Fredholm index limit operators band-dominated operators Wiener-Hopf operators 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  1. 1.Instituto Politechnico NationalMexicoMexico
  2. 2.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

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