## Abstract and Applied Analysis

### Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

#### Abstract

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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 162769, 10 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512106

Digital Object Identifier
doi:10.1155/2013/162769

Mathematical Reviews number (MathSciNet)
MR3124035

Zentralblatt MATH identifier
1297.42015

#### Citation

Bahri, Mawardi; Ashino, Ryuichi; Vaillancourt, Rémi. Convolution Theorems for Quaternion Fourier Transform: Properties and Applications. Abstr. Appl. Anal. 2013 (2013), Article ID 162769, 10 pages. doi:10.1155/2013/162769. https://projecteuclid.org/euclid.aaa/1393512106

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