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 ,
$$ \mathop {\sup }\limits_{x \in \mathbb{R}^n } \left| {x^\alpha \partial _x^\beta u(x)} \right| < + \infty . $$


Quadratic Form Classical Analysis Real Vector Space Symplectic Group Maslov Index 
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© 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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