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Abstract

Let n≥1 be an integer. The Schwartz space S(ℝ n ) is defined as the space of C functions u from ℝ n to ℂ such that, for all multi-indices1 α, β∈ℕ n ,
$$ \mathop {\sup }\limits_{x \in \mathbb{R}^n } \left| {x^\alpha \partial _x^\beta u(x)} \right| < + \infty . $$

Keywords

Quadratic Form Classical Analysis Real Vector Space Symplectic Group Maslov Index 
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

© Birkhäuser Verlag AG 2010

Authors and Affiliations

  • Nicolas Lerner
    • 1
  1. 1.Projet Analyse fonctionnelle Institut de Mathématique de JussieuUniversité Pierre et Marie Curie (Paris VI)Paris cedex 05France

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