Abstract:
This paper generalizes part of the author's previous results.
Let $L$ be a multilinear differential operator with constant coefficients.
The fundamental solution $\phi$
supported in a convex cone of a linear space $U$
is piecewise polynomial.
Choose a basis in the space $T$ of polynomials
and consider the corresponding set of convex cones in the space $U$.
We claim
that
$\phi (x)$ is equal to a sum of basis elements in $T$,
with
the sum being taken over those elements
for which the corresponding cones contain $x$.
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