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 \(y \to 0\), \(y \in C\), 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 are obtained.
scientific article; zbMATH DE number 761850