KdV & KAM pp 177-186 | Cite as

Kuksin’s Lemma

  • Thomas Kappeler
  • Jürgen Pöschel
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics book series (MATHE3, volume 45)


We consider the following first order partial differential equation coming up in the proof of the classical KAM theorem:
$$ - i\partial _\omega u + \lambda u + b\left( x \right)u = f,x \in {\Bbb T}^n $$
for functions on the torus T n = ℝ n /2π n , where
$$ \partial _\omega = \sum\limits_{v = 1}^n {\omega _v \partial _{xv} } ,\omega = \left( {\omega _1 , \ldots ,\omega _n } \right) \in {\Bbb R}^n $$


Trigonometric Polynomial Oscillatory Integral Frequency Vector Order Partial Differential Equation Approximation Lemma 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Thomas Kappeler
    • 1
  • Jürgen Pöschel
    • 2
  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland
  2. 2.Fakultät Mathematik und PhysikUniversität StuttgartStuttgartGermany

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