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).
KeywordsLimit Operator Pseudodifferential Operator Essential Spectrum Singular Integral Operator Fredholm Operator
Unable to display preview. Download preview PDF.