Convolution theorems for quaternion Fourier transform: properties and applications
type: Item
instance of: scholarly article
title: Convolution theorems for quaternion Fourier transform: properties and applications
zbMATH Open document ID: 1297.42015
DOI: 10.1155/2013/162769
author: Mawardi Bahri
author: Rémi Vaillancourt
author: Ryuichi Ashino
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: Summary: General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework.
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 42B37
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 6306080
zbMATH Keywords: quaternion Fourier transform
zbMATH Keywords: convolution
zbMATH Keywords: hypoellipticity
zbMATH Keywords: heat equation
zbMATH Keywords: quaternion algebra
Wikidata QID: Q58915400
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/162769
OpenAlex ID: W2039603470
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description: scientific article; zbMATH DE number 6306080