Pseudodifferential Operators

  • Michael E. Taylor
Part of the Applied Mathematical Sciences book series (AMS, volume 116)


In this chapter we discuss the basic theory of pseudodifferential operators as it has been developed to treat problems in linear PDE. We define pseudodifferential operators with symbols in classes denoted S ρ,δ m introduced by L. Hörmander. In §2 we derive some useful properties of their Schwartz kernels. In §3 we discuss adjoints and products of pseudodifferential operators. In §4 we show how the algebraic properties can be used to establish the regularity of solutions to elliptic PDE with smooth coefficients. In §5 we discuss mapping properties on L 2 and on the Sobolev spaces H s . In §6 we establish Gårding’s inequality.


Pseudodifferential Operator Integral Kernel Solution Operator Layer Potential Principal Symbol 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Michael E. Taylor
    • 1
  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

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