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

${\displaystyle |D^{\alpha }g(x)|\leq CR^{k}(k!)^{\sigma }}$

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.

See also

• Denjoy–Carleman theorem

References

• Gevrey, Maurice (1918), "Sur la nature analytique des solutions des équations aux dérivées partielles. Premier mémoire.", Annales Scientifiques de l'École Normale Supérieure, 3, 35: 129–190