Integral Equations and Operator Theory

, Volume 57, Issue 2, pp 263–281

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

Authors

    • Instituto Politechnico National
    • Fachbereich MathematikTechnische Universität Darmstadt
Article

DOI: 10.1007/s00020-006-1456-y

Cite this article as:
Rabinovich, V.S. & Roch, S. Integr. equ. oper. theory (2007) 57: 263. doi:10.1007/s00020-006-1456-y

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 47A53Secondary 47G1045E10

Keywords.

Fredholm indexlimit operatorsband-dominated operatorsWiener-Hopf operators

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006