Gevrey class
In mathematics, the Gevrey classes on a domain , introduced by Maurice Gevrey, are spaces of functions 'between' the space of analytic functions  and the space of smooth (infinitely differentiable) functions . In particular, for , the Gevrey class , consists of those smooth functions  such that for every compact subset  there exists a constant , depending only on , such that

Where  denotes the partial derivative of order  (see multi-index notation). When ,  coincides with the class of analytic functions , but for  there are compactly supported functions in the class that are not identically zero (an impossibility in ). It is in this sense that they interpolate between  and . The Gevrey classes find application in discussing the smoothness of solutions to certain partial differential equations: Gevrey originally formulated the definition while investigating the homogeneous heat equation, whose solutions are in . Application 

Gevrey functions are used in control engineering for trajectory planning. A typical example is the function 

with 

and Gevrey order

See also

Denjoy–Carleman theorem

References

Smooth functions