The existence of decompositions of the form $f=P\cdot q+r$ with $P_k^{ \ast}\left( D\right) r=0$, where $f$ is entire, $P$ a polynomial and $P^{ \ast}_k$ the principal part of $P$ with its coefficients conjugated, was achieved in \cite{ AlRe23} under certain restrictions on the order of $f$. Here we prove uniqueness, thereby obtaining Fischer decompositions, under conditions that sometimes match those required for existence, and sometimes are more restrictive, depending on the parameters involved.
Categories: math.AP