Article

Integral Equations and Operator Theory

, Volume 57, Issue 2, pp 263-281

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

  • Vladimir S. RabinovichAffiliated withInstituto Politechnico National Email author 
  • , Steffen RochAffiliated withFachbereich Mathematik, Technische Universität Darmstadt Email author 

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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 \(L^p \,(\user2{\mathbb{R}})\) 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