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Quaternionic continuous wavelet transform on a quaternionic Hilbert space

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Abstract

In this paper we consider the new concept of the quaternionic unitary representation of a locally compact group to the unitary group of a quaternionic Hilbert space, and study its properties. Also, we establish a continuous wavelet transform by means of a special case of such representations to extend the continuous wavelet transform related to semidirect product groups. The results may be useful in development of wavelet theory.

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Acknowledgements

The author would like to express the most sincere gratitude to the memory of Professor Syed Twareque Ali from Concordia University, for the valuable discussions on the initial version of the manuscript. Also, the author would like to thank the reviewers for their comments and suggestions on the paper. This research was supported by a grant from Ferdowsi University of Mashhad; No. 2/43973.

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Correspondence to M. Fashandi.

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Fashandi, M. Quaternionic continuous wavelet transform on a quaternionic Hilbert space. RACSAM 112, 1049–1057 (2018). https://doi.org/10.1007/s13398-017-0409-4

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  • DOI: https://doi.org/10.1007/s13398-017-0409-4

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