Eigenfunctions of Laplacian by boundedness conditions in bounded hyperfunctions and distributions.
It is proved that any Banach valued distribution on a bounded set can be extended to all of if and only if it is a derivative of a uniformly continuous function. A similar result is given for distributions on an unbounded set. An example shows that this does not extend to Frechet valued distributions. This relies on the fact that a Banach valued distribution is locally a derivative of a uniformly continuous function. For sake of completeness, a global representation of a Banach valued distribution...