Weyl's theorem
Encyclopedia
In mathematics
, Weyl's theorem or Weyl's lemma might refer to one of a number of results of Hermann Weyl
. These include
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, Weyl's theorem or Weyl's lemma might refer to one of a number of results of Hermann Weyl
Hermann Weyl
Hermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...
. These include
- the Peter–Weyl theoremPeter–Weyl theoremIn mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not necessarily abelian. It was initially proved by Hermann Weyl, with his student Fritz Peter, in the setting of a compact topological group G...
- results derived from the unitarian trickUnitarian trickIn mathematics, the unitarian trick is a device in the representation theory of Lie groups, introduced by for the special linear group and by Hermann Weyl for general semisimple groups. It applies to show that the representation theory of some group G is in a qualitative way controlled by that...
on representation theoryRepresentation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
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 lemmaWeyl's lemma (Laplace equation)In mathematics, Weyl's lemma is a result that provides a "very weak" form of the Laplace equation. It is named after the German mathematician Hermann Weyl.-Statement of the lemma:...
on the "very weak" form of the Laplace equation - results estimating Weyl sums in the theory of exponential sumExponential sumIn mathematics, an exponential sum may be a finite Fourier series , or other finite sum formed using the exponential function, usually expressed by means of the functione = \exp.\,...
s - Weyl's inequality