Some functional equations in the spaces of generalized functions
type: Item
instance of: scholarly article
title: Some functional equations in the spaces of generalized functions
zbMATH Open document ID: 1035.39015
author: Shinyoung Lee
author: Jaeyoung Chung
published in: Aequationes Mathematicae
publication date: 2003-11-17T00:00:00Z
review text: The authors consider some classical functional equations (Cauchy, Pexider, Jensen, D'Alembert, quadratic) in the spaces of generalized functions such as the Schwartz distributions and the Sato hyperfunctions. These equations written for the functions from \(\mathbb{R}^n\) to \(\mathbb{C}\) themselves make no sense in the spaces of generalized functions. The authors extend these functional equations to the spaces of generalized functions making use of the tensor product and pullback of generalized functions as in \textit{S.-Y. Chung's} paper [ibid. 59, 108--123 (2000; Zbl 0945.39013)]. These extended functional equations are solved in the spaces of tempered distributions and Fourier hyperfunctions. In the final part of the paper the authors study also the ``nonhomogeneous'' additive functional equation.
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 46F10
zbMATH DE Number: 2004952
zbMATH Keywords: Gauss transforms
zbMATH Keywords: Heat kernel
zbMATH Keywords: distributions
zbMATH Keywords: hyperfunctions
zbMATH Keywords: functional equations
zbMATH Keywords: Cauchy functional equation
zbMATH Keywords: Pexider functional equation
zbMATH Keywords: Jensen functional equation
zbMATH Keywords: D'Alembert functional equation
zbMATH Keywords: quadratic functional equation
zbMATH Keywords: generalized functions
zbMATH Keywords: Schwartz distributions
zbMATH Keywords: Sato hyperfunctions
zbMATH Keywords: tensor product
zbMATH Keywords: tempered distributions
zbMATH Keywords: Fourier hyperfunctions
zbMATH Keywords: nonhomogeneous additive functional equation
reviewed by: Borislav Crstici
MaRDI profile type: Publication
full work available at URL: s00010-003-2657-y
OpenAlex ID: W2040110406
DOI: 10.1007/S00010-003-2657-Y
description: scientific article; zbMATH DE number 2004952