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

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

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.

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

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Gevrey class

See also

References