The author offers and discusses general ideas on an extension of Ehrenpreis’ fundamental principle to the multi-complex setting. Any solution of a system of polynomial differential operators with constant coefficients permits a integral representation of the form \[ f(x)= \sum^t_{k=1} \int_{V_k} Q_k(x)\exp(iz\cdot x)\,d\mu_k(z) \] with polynomials \(Q_k\) and bounded measures \(\mu_k\) taken over a finite number of algebraic varieties in a localizable analytically uniform space (i.e., a space of analytic functions with exponential growth). This theory should be possible to apply to generalized Cauchy-Riemann systems of bi- and multicomplex holomorphic functions.
For the entire collection see [Zbl 1253.30004].