Abstract
The Weinstein transform satisfies some uncertainty principles in a similar way to the Euclidean Fourier transform. Donoho–Stark’s uncertainty principle is obtained for the Weinstein transform.
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Achak, A., Daher, R.J.: Benedicks–Amrein–Berthier type theorem related to Opdam–Cherednik transform. J. Pseudo-Differ. Oper. Appl. (2017). https://doi.org/10.1007/s11868-017-0189-9
Achak, A., Daher, R.: Benedicks-Amrein-Berthier type theorem related to Weinstein transform. Anal. Math. 43(4), 511–521 (2017). https://doi.org/10.1007/s10476-017-0201-x
Achak, A., Daher, R., Lahlali, H.: Beurling’s theorem for Bessel-Struve transform. C.R. Math. 354(1), 81–85 (2016). https://doi.org/10.1016/j.crma.2015.09.013
Benedicks, M.: On Fourier transforms of function supported on sets of finite Lebesgue measure. J. Math. Anal. Appl. 106, 180–183 (1985)
Beurling, A.: The Collect Works of Arne Beurling. Birkhauser, Boston (1989)
Cowling, M.G., Price, J.F.: Generalizations of Heisenberg’s inequality. In: Mauceri, G., Ricci, F., Weiss, G. (eds.) Harmonic Analysis. Lecture Notes in Mathematics, vol. 992, pp. 443–449. Springer, Berlin (1983)
Donoho, D.L., Stark, P.B.: Uncertainty principles and signal recovery. SIAM J. Appl. Math. 49, 906–931 (1989)
Folland, G.B., Sitaram, A.: The uncertainty principle: a mathematical survey. J. Fourier Anal. Appl. 3(3), 207–238 (1997)
Ghazwani, J., Soltani, F.: A variation of the Lp uncertainty principles for the Fourier transform. In: Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, vol. 42, no. 1, pp. 10–24 (2016)
Hardy, G.H.: A theorem concerning Fourier transform. J. Lond. Math. Soc. 8, 227–231 (1933)
Mejjaoli, H., Salhi, M.: Uncertainty principles for the Weinstein transform. Czech. Math. J. 61(136), 941–974 (2011)
Stein, E.M.: Interpolation of linear operators. Trans. Am. Math. Soc. 83, 482–492 (1956)
Thangavelu, S.: An Introduction to the Uncertainty Principle. Progress in Mathematics, vol. 217. Birkhäuser, Basel (2004)
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Abouelaz, A., Achak, A., Daher, R. et al. Quantitative uncertainty principles for the Weinstein transform. Bol. Soc. Mat. Mex. 25, 375–383 (2019). https://doi.org/10.1007/s40590-018-0197-7
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DOI: https://doi.org/10.1007/s40590-018-0197-7