Theorem of Burnside and Molien: For finite dimensional groups,
all irreps can be obtained from tensor products of a faithful finite dim
irrep
Peter-Weyl theorem: For any group element ,
one can find an irreducible representation
Edge-of-the-wedge theorem: if two holomorphic functions on two
wedges give same continuous function on the common edge, then they
are analytic continuation of each other. (Example: Suppose that f is
a continuous complex-valued function on the complex plane that is
holomorphic on the upper half-plane, and on the lower half-plane.
Then it is holomorphic everywhere.)
The hypothesis of weak conformal invariance says that the
Euclidean Green functions should be invariant under conformal transformations
Jacobian Conjecture states that a polynomial function
is invertible, and its inverse is polynomial, if and only if the determinant
of the Jacobian matrix is a non-zero constant.1
Fubini’s theorem states that a double integral can be computed as
an iterated integral under certain conditions such as convergence.
Sokhotski–Plemelj theorem relates principle value to limits of
other functions; common example is the delta function written as
principle value and a limit.