Artin conductor

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

$|D^{\alpha }g(x)|\le C{R}^k{k}^{\sigma k}$

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.

See also

• Denjoy–Carleman theorem

References

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