In this paper we prove that the projective dimension of ${ℳ}_n=R^4/⟨A_n⟩$ is $2n-1$, where $R$ is the ring of polynomials in $4n$ variables with complex coefficients, and $⟨A_n⟩$ is the module generated by the columns of a $4\times 4n$ matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of $n$ quaternionic variables. As a corollary we show that the sheaf $ℛ$ of regular functions has flabby dimension $2n-1$, and we prove a cohomology vanishing theorem for open...

In this paper we use Nachbin’s holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables