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 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 .
When, coincides with the class of analytic functions, but for there are compactly supported functions in the class that are not identically zero. 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