On the Fourier-Laplace representation of analytic functions in tube domains

Let $C$ denote an acute convex open cone in $\mathbb{R}^n$ with an apex at the origin and let $T(C) = \mathbb{R}^n + iC$ be the corresponding tube in $\mathbb{C}^n$. We define a space of holomorphic functions $f(z)$ of exponential type in $T(C)$ which have boundary values $f_0(x)$, as $y\rightarrow 0, y\in C$, satisfying some inequality. We obtain Fourier- Laplace integral representation of these functions. As a consequence a weighted version of the edge of the wedge theorem and Fourier-Laplace representation of entire functions of exponential type (with more general growth characteristics than in [2]) are obtained.