Pseudodifferential Operators of Type (ρ,δ)

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


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.


Compact Subset Bounded Linear Operator Pseudodifferential Operator Principal Symbol Positive Continuous Function 
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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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