On the Fourier-Laplace representation of analytic functions in tube domains
type: Item
instance of: scholarly article
title: On the Fourier-Laplace representation of analytic functions in tube domains
zbMATH Open document ID: 0823.32001
published in: Collectanea Mathematica
publication date: 1995-11-06T00:00:00Z
full work available at URL: https://eudml.org/doc/39762
review text: 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.
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32A07
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 32A15
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 46F20
zbMATH DE Number: 761850
zbMATH Keywords: Laplace transform
zbMATH Keywords: tube domains
zbMATH Keywords: Fourier transform
zbMATH Keywords: holomorphic functions
zbMATH Keywords: integral representation
zbMATH Keywords: edge of the wedge theorem
zbMATH Keywords: entire functions
zbMATH Keywords: exponential type
author: Il'dar Khamitovich Musin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 761850