Holomorphic functions of polynomial growth on abelian coverings of a compact complex manifold (Q1271409)

Let \(M\) be a compact complex manifold and \(p:M_G\to M\) be a regular covering over \(M\) with a free abelian transformation group \(G\). The author proves that under some assumptions on \(G\) the space \({\mathcal P}_l(M_G)\) of holomorphic functions on \(M_G\) of \(l\)-polynomial growth is finite dimensional and is linearly imbedded into the corresponding space \({\mathcal P}_l(\mathbb C^N)\) of holomorphic polynomials on \(\mathbb C^N\) with \(N=\frac 12 \text{ rank}(G)\).