Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

Mawardi Bahri, Ryuichi Ashino and Rémi Vaillancourt

Abstract and Applied Analysis, 2013, vol. 2013, 1-10

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.

Date: 2013
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2013/162769.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2013/162769.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:162769

DOI: 10.1155/2013/162769

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().