  Let $V = < p_{ij}(x)e^{\la_ix}, i=1,...,n, j=1, ..., N_i >$ be a space of
quasi-polynomials of dimension $N=N_1+...+N_n$. Define the regularized
fundamental operator of $V$ as the polynomial differential operator $D =
\sum_{i=0}^N A_{N-i}(x)\p^i$ annihilating $V$ and such that its leading
coefficient $A_0$ is a polynomial of the minimal possible degree. We construct
a space of quasi-polynomials $U = < q_{ab}(u)e^{z_au} >$ whose regularized
fundamental operator is the differential operator $\sum_{i=0}^N u^i
A_{N-i}(\partial_u)$. The space $U$ is constructed from $V$ by a suitable
integral transform. Our integral transform corresponds to the bispectral
involution on the space of rational solutions (vanishing at infinity) to the KP
hierarchy, see \cite{W}.
  As a corollary of the properties of the integral transform we obtain a
correspondence between critical points of the two master functions associated
with the $(\glN,\glM)$ dual Gaudin models as well as between the corresponding
Bethe vectors.
