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High Quality Content by WIKIPEDIA articles! 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 results 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 partial differential equations and hypoellipticity Weyl's lemma on the "very weak" form of the Laplace equation results estimating Weyl sums in the theory of exponential sums Weyl's inequality.