Pseudo-Differential Operators of Principal Type

  • Lars Hörmander
Chapter
Part of the Grundlehren der mathematischen Wissenschaften book series (CLASSICS)

Summary

In Section 10.4 we saw that the strength of a differential operator with constant coefficients in ℝ n is determined by the principal part p if and only if p=0 implies dp≠0 in ℝ n \0. Such operators were said to be of principal type. The purpose of this chapter is to study general operators P∈Ψ phg m (X) on a manifold X assuming that the condition dp ≠0 when p =0 is valid in a suitably strengthened form which makes the properties of p independent of lower order terms.

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Notes

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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Lars Hörmander
    • 1
  1. 1.Department of MathematicsUniversity of LundLundSweden

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