Pseudodifferential Operators

  • Vladimir Rabinovich
  • Bernd Silbermann
  • Steffen Roch
Part of the Operator Theory: Advances and Applications book series (OT, volume 150)


In this chapter, we are going to study the Fredholmness of pseudodifferential operators on ℝN. Again, our strategy is to discretize these operators in a suitable manner in order to get operators which live on a discrete l2-space. In the situation at hand, it is convenient to perform this discretization both with respect to the variable x ∈ ℝN and with respect to the co-variable ξ ∈ ℝN in the Fourier image. One advantage of this discretization is that P-Fredholm operators on the discrete l2-space correspond to common Fredholm operators on L2(ℝN).


Limit Operator Pseudodifferential Operator Essential Spectrum Singular Integral Operator Fredholm Operator 
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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Vladimir Rabinovich
    • 1
  • Bernd Silbermann
    • 2
  • Steffen Roch
    • 3
  1. 1.Instituto Politécnico NacionalESIME ZacatencoMexico, D.F.USA
  2. 2.Department of MathematicsTechnical University of ChemnitzChemnitzGermany
  3. 3.Department of MathematicsTechnical University of DarmstadtDarmstadtGermany

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