Complements: Symplectic Aspects

  • André Martinez
Part of the Universitext book series (UTX)


For u = (u x , u ξ ) and υ = (υ x , υ ξ ) ∈ R 2n , we set
$$\sigma (u,\upsilon ) = {u_\xi } \cdot {u_x} - {u_x}{\upsilon _\xi } = \langle ((\begin{array}{*{20}{c}} 0&I \\ { - I}&0 \end{array})(\begin{array}{*{20}{c}} {{u_x}} \\ {{u_\xi }} \end{array})(\begin{array}{*{20}{c}} {{\upsilon _x}} \\ {\upsilon \xi } \end{array}))\rangle .$$


Symplectic Form Pseudodifferential Operator Pseudo Differential Operator Canonical Transformation Principal Symbol 
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 2002

Authors and Affiliations

  • André Martinez
    • 1
  1. 1.Department of MathematicsUniversity of BolognaBolognaItaly

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