title: Weyl's theorem
text: # Weyl's theorem
  
  In mathematics, Weyl's theorem or Weyl's lemma might refer to one of a number of results of Hermann Weyl. These include
  
  * the Peter–Weyl theorem
  * Weyl's theorem on complete reducibility, results originally derived from the unitarian trick on representation theory of semisimple groups and semisimple Lie algebras
  * Weyl's theorem on eigenvalues
  * Weyl's criterion for equidistribution (Weyl's criterion)
  * Weyl's lemma on the hypoellipticity of the Laplace equation
  * results estimating Weyl sums in the theory of exponential sums
  * Weyl's inequality
  * Weyl's criterion for a number to be in the essential spectrum of an operator
  