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KdV & KAM pp 177-186 | Cite as

Kuksin’s Lemma

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

Abstract

We consider the following first order partial differential equation coming up in the proof of the classical KAM theorem:
$$ - i\partial _\omega u + \lambda u + b\left( x \right)u = f,x \in {\Bbb T}^n $$
(23.1)
for functions on the torus T n = ℝ n /2π n , where
$$ \partial _\omega = \sum\limits_{v = 1}^n {\omega _v \partial _{xv} } ,\omega = \left( {\omega _1 , \ldots ,\omega _n } \right) \in {\Bbb R}^n $$
.

Keywords

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