Abstract
In this paper, we provide the Heisenberg’s inequality and the Hardy’s theorem for the two-sided quaternion Fourier transform.
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Bülow, T.: Hypercomplex spectral signal representations for the processing and analysis of images. Ph.D. Thesis, Institut für Informatik und Praktische Mathematik, University of Kiel, Germany (1999)
Chen, L.P., Kou, K.I., Liu, M.S.: Pitt’s inequality and the uncertainty principle associated with thequaternion Fourier transform. J. Math. Anal. Appl. 423, 681–700 (2015)
Christensen, J.G.: Uncertainty Principles. Master’s Thesis, Institute for Mathematical Sciences, University of Copenhagen (2003)
De Bie, H.: New techniques for two-sided quaternion Fourier transform, In: Procedings of AGACSE (2012)
Eckhard, M., Hitzer, S.: Quaternion Fourier transform on quaternion fields and generalizations (2013). arXiv:1306.1023v1 [math.RA]
Ell, T.A.: Quaternion-Fourier transforms for analysis of two-dimensional linear time-invariant partial differential systems. In: Proceeding of the 32nd Conference on Decision and Control, San Antonio, pp. 1830–1841 (1993)
Hardy, G.H.: A theorem concerning Fourier transform. J. Lond. Math. Soc. 8, 227–231 (1933)
Pei, S.C., Ding, J.J., Chang, J.H.: Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT. IEEE Trans. Signal Process. 49(11), 2783–2797 (2001)
Pierce, L.B.: Hardy Functions. Undergraduate Junior Paper , Princeton University, University (2001)
Sitaram, A., Sundari, M.: An analogue of Hardy’s theorem for very rapidly decreasing functions on semi-simple Lie groups. Pac. J. Math. 177, 187–200 (1997)
Weyl, Gruppentheorie, Quantenmechanik, S., Hirzel, Leipzig (1928). Revised English edition: The Theory of Groups and Qunantum Mechans, Methuen, London (1931); Reprinted by Dover, New York (1950)
Yang, Y., Dang, P., Qian, T.: Tighter uncertainty principles based on quaternion Fourier transform. Adv. Appl. Clifford Algebras 26, 479–497 (2016)
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El Haoui, Y., Fahlaoui, S. The Uncertainty Principle for the Two-Sided Quaternion Fourier Transform. Mediterr. J. Math. 14, 221 (2017). https://doi.org/10.1007/s00009-017-1024-5
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DOI: https://doi.org/10.1007/s00009-017-1024-5