Noncompensation of the singularities of functions that are holomorphic in tubular cones (Q1374966)

Let \(C\) be an open acute cone in \(\mathbb{R}^n\) with vertex at the origin, and let \(H(C)\) be the class of functions holomorphic in the tubular domain \(T^C= \mathbb{R}^n+ iC\), \(z= x+ iy\), \(x\in\mathbb{R}^n\), \(y\in C\) and satisfying the estimate \(| f(z) |\leq M{(1+ | z|^a \over [\Delta_C (y)]^b}\), \(z\in T^C\) for some \(a,b\) and \(M\). Here \(\Delta_C(y)\) is the distance from \(y\) to the boundary of the \(C\) cone. The authors consider \(m\) functions \(f_i\in H(C_i)\), where the cones \(C_i\) have nonempty intersection and are such that the convex hull of their union is \(\mathbb{R}^n\). The authors formulate results concerning asymptotic behavior of each of the \(f_i\) as \(z\to 0\) in \(T^{C_i}\) from the corresponding asymptotic behavior of their sum in the common domain of analyticity.