Let A be the square matrix \((a_{i_ j})\) U be a domain in \(C^ k\), and H(u) be the space of holomorphic functions in U with the locally uniform convergence topology. The author proves that under some stated conditions on the matrix A, and the domain U, the invariant subspace \(W\subset H(U)\) admits a spectral synthesis. Also a Mittag-Leffler type theorem for invariant subspaces is proven in the article.