Special issue: New theories and technological advancesNo Access

Continuous quaternion fourier and wavelet transforms

Mawardi Bahri

Department of Mathematics, Universitas Hasanuddin, Makassar 90245, Indonesia

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Ryuichi Ashino

Division of Mathematical Sciences, Osaka Kyoiku University, Osaka 582-8582, Japan

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, and

Rémi Vaillancourt

Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada K1N 6N5, Canada

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https://doi.org/10.1142/S0219691314600030Cited by:28 (Source: Crossref)

Abstract

A two-dimensional (2D) quaternion Fourier transform (QFT) defined with the kernel is proposed. Some fundamental properties, such as convolution, Plancherel and vector differential theorems, are established. The heat equation in quaternion algebra is presented as an example of the application of the QFT to partial differential equations. The wavelet transform is extended to quaternion algebra using the kernel of the QFT.

Keywords:

AMSC: 15A66, 42B10, 30G35

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