Example of an -harmonic function which is not on a dense subset.
Examples of functions -extendable for each finite, but not -extendable
In Example 1, we describe a subset X of the plane and a function on X which has a -extension to the whole for each finite, but has no -extension to . In Example 2, we construct a similar example of a subanalytic subset of ; much more sophisticated than the first one. The dimensions given here are smallest possible.
Extending times differentiable functions of several variables
It is shown that times Peano differentiable functions defined on a closed subset of and satisfying a certain condition on that set can be extended to times Peano differentiable functions defined on if and only if the th order Peano derivatives are Baire class one functions.
Extending o-minimal Fréchet derivatives
We investigate several extension properties of Fréchet differentiable functions defined on closed sets for o-minimal expansions of real closed fields.
Extension of differentiable functions