Dembski's calculations show how a simple smooth function cannot gain information.

The space of smooth functions on any compact manifold is nuclear.

See here for another example of a non-analytic smooth function.

A 0-form is defined to be a smooth function f.

In that example, we can consider test functions F, which are smooth functions with support not including the point 0.

This has the intuitive interpretation as the set of points at which a distribution fails to be a smooth function.

These are necessarily smooth functions of compact support in Ω.

The design of continuous or smooth refinable functions is not obvious.

Over , comes to differ from identity by a smooth function.

The flow can either be given in a finite representation or as a smooth function.