Gevrey class

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In mathematics, the Gevrey class Gσ, 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 Dα (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[edit]


  • 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