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Pseudodifferential Operators of Type (ρ,δ)

  • François Treves
Part of the The University Series in Mathematics book series (USMA)

Abstract

In order to generalize the parametrix construction of Section 1, Chapter I to certain classes of nonelliptic (yet hypoelliptic) equations, one must enlarge the pool of amplitudes that one is willing to use. Such a construction is carried out in Section 1 of this chapter. In an embryonic form it was first, I believe, attempted in Treves [1]. The classes of symbols best suited for such an extension were introduced and described by Hörmander in [3], and given the name S ρ,δ classes. Roughly speaking the properties of pseudodifferential operators of type (1, 0), our “standard” pseudodifferential operators (Chapter I), generalize well to type (ρ, δ) as long as we keep 0 ≤ δ < ½ < ρ, as shown in Section 2.

Keywords

Compact Subset Bounded Linear Operator Pseudodifferential Operator Principal Symbol Positive Continuous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • François Treves
    • 1
  1. 1.Rutgers UniversityNew BrunswickUSA

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