  Helmholtz decomposition theorem for vector fields is presented usually with
too strong restrictions on the fields. Based on the work of Blumenthal of 1905
it is shown that the decomposition of vector fields is not only possible for
asymptotically weakly decreasing vector fields, but even for vector fields,
which asymptotically increase sublinearly. Use is made of a regularizatin of
the Greens function and the mathematics of the proof is formulated as simply as
possible. We also show a few examples for the decomposition of vector fields
including the electric dipole radiation.
