Abstract
This paper is devoted to studying uncertainty principle of Heisenberg type for signals on the unit sphere in the Clifford algebra setting. In the Clifford algebra setting we propose two forms of uncertainty principle for spherical signals, of which both correspond to the strongest form of uncertainty principle for periodic signals. The lower-bounds of the proven uncertainty principles are in terms of a scalar-valued phase derivative.
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Communicated by Frank Sommen.
This work was supported by Macao Science and Technology Development Fund, MSAR. Ref. 045/2015/A2; National Natural Science Funds for Young Scholars: 11701597; Macao Government FDCT 098/2012/A3; University of Macau Multi-Year Research Grant (MYRG) MYRG116(Y1-L3)-FST13-QT; NSFC grant 11571083.
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Dang, P., Qian, T. & Chen, Q. Uncertainty Principle and Phase–Amplitude Analysis of Signals on the Unit Sphere. Adv. Appl. Clifford Algebras 27, 2985–3013 (2017). https://doi.org/10.1007/s00006-017-0808-9
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DOI: https://doi.org/10.1007/s00006-017-0808-9