Proceedings of the Centre for Mathematics and its Applications

Translation-Invariant Clifford Operators

Jeff Hogan and Andrew J. Morris

Full-text: Open access

Abstract

This paper is concerned with quaternion-valued functions on the plane and operators which act on such functions. In particular, we investigate the space $L^2(\mathbb{R}^2, \mathbb{H})$ of square-integrable quaternion-valued functions on the plane and apply the recently developed Clifford-Fourier transform and associated convolution theorem to characterise the closed translation-invariant submodules of $L^2(\mathbb{R}^2, \mathbb{H})$ and its bounded linear translation-invariant operators. The Clifford-Fourier characterisation of Hardy-type spaces on $\mathbb{R}^d$ is also explored.

Article information

Source
AMSI International Conference on Harmonic Analysis and Applications. Xuan Duong, Jeff Hogan, Chris Meaney, and Adam Sikora, eds. Proceedings of the Centre for Mathematics and its Applications, v. 45. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 2013), 48-62

Dates
First available in Project Euclid: 3 December 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1417630505

Mathematical Reviews number (MathSciNet)
MR3424867

Zentralblatt MATH identifier
1337.42005

Citation

Hogan, Jeff; Morris, Andrew J. Translation-Invariant Clifford Operators. AMSI International Conference on Harmonic Analysis and Applications, 48--62, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 2013. https://projecteuclid.org/euclid.pcma/1417630505


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