Stein factorization [SEP] named after
Stein factorization
In algebraic geometry, the Stein factorization, introduced by for the case of complex spaces, states that a proper morphism can be factorized as a composition of a finite mapping and a proper morphism with connected fibers. Roughly speaking, Stein factorization contracts the connected components of the fibers of a mapping to points.
One version for schemes states the following:
Let "X" be a scheme, "S" a locally noetherian scheme and formula_1 a proper morphism. Then one can write
where formula_3 is
These include "Stein interpolation" (a variable-parameter version of complex interpolation), the "Stein maximal principle" (showing that under many circumstances, almost everywhere convergence is equivalent to the boundedness of
a maximal function), "Stein complementary series representations", "Nikishin–Pisier–Stein factorization" in operator theory, the "Tomas–Stein restriction theorem" in Fourier analysis, the "Kunze–Stein phenomenon" in convolution on semisimple groups, the Cotlar–Stein lemma concerning the sum of almost orthogonal