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 Weyl's law that describes the asymptotic behavior of large eigenvalues of the Laplace–Beltrami operator