Wiener Algebras of Operators, and Applications to Pseudodifferential Operators

  • Vladimir S. Rabinovich

    Escuelo Superior de Mat y Fis del IPN, México, D.f., Mexico
  • Steffen Roch

    Technische Hochschule Darmstadt, Germany

Abstract

We introduce a Wiener algebra of operators on which contains, for example, all pseudodifferential operators in the Hörmander class . A discretization based on the action of the discrete Heisenberg group associates to each operator in this algebra a band-dominated operator in a Wiener algebra of operators on . The (generalized) Fredholmness of these discretized operators can be expressed by the invertibility of their limit operators. This implies a criterion for the Fredholmness on of pseudodifferential operators in in terms of their limit operators. Applications to Schrödinger operators with continuous potential and other partial differential operators are given.

Cite this article

Vladimir S. Rabinovich, Steffen Roch, Wiener Algebras of Operators, and Applications to Pseudodifferential Operators. Z. Anal. Anwend. 23 (2004), no. 3, pp. 437–482

DOI 10.4171/ZAA/1207