Smooth functions

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 . (Wikipedia).

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Related pages

Analytic function | Multi-index notation | Smoothness