Gevrey class

In mathematics, the Gevrey class G^σ, introduced by Gevrey (1918), consists of the smooth functions g on Rⁿ such that on every compact subset K there are constants C and R with

for multi-indices α, such that |α| = k, and corresponding differential operators D^α (see multi-index notation); and x restricted to lie in the compact set K.

When σ = 1 this class is the same as the class of analytic functions. For σ > 1 there are compactly supported functions in the class that are not identically zero.