Some uncertainty inequalities related to the multivariate Laguerre function. (English) Zbl 1448.42018
Summary: In this paper, an analogous of the Heisenberg’s inequality is established and three inequalities that constitute local uncertainty principle for the generalized Fourier-Laguerre transform in several variables are developed.
MSC:
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 44A35 | Convolution as an integral transform |
| 35K08 | Heat kernel |
| 26D15 | Inequalities for sums, series and integrals |
References:
| [1] | De Bruijn NG. Uncertainty principle in Fourier analysis. In: Inequalities, Shisha O (editor). Proceedings of Symposium held at Wright-Patterson air force base; Ohio, USA 1967. pp. 57-71. |
| [2] | Faris WG. Inequalities and uncertainty principles. Journal of Mathematical Physics 1978; 19: 461-466. doi: 10.1063/1.523667 |
| [3] | Ghobber S, Jaming P. Uncertainty principles for integral operators. Studia Mathematica 2014; 220 (3): 197-220. doi: 10.4064/sm-220-3-1 · Zbl 1297.42018 |
| [4] | Guliyev VS. Polar coordinates in Laguerre hypergroup. Khazar Journal of Mathematics 2006; 2 (3): 11-20. |
| [5] | Heisenberg W. Uber den anschaulichen inhalt der quantentheoretiscchen kinematic und mechanik. Zeitschrift für Physik 1927; 43: 172-198 (in German). · JFM 53.0853.05 |
| [6] | Huang J, Liu H. The weak type (1,1) estimates of maximal functions on the Laguerre hypergroup. Canadian Mathematical Bulletin 2010; 53 (3): 491-502. doi: 10.4153/cmb-2010-058-6 · Zbl 1204.43007 |
| [7] | Kamoun L, Selmi R. Harmonic analysis associated to the multivariate Laguerre function. Mediterranean Journal of Mathematics 2018; 15 (2): Article 39. doi: 10.1007/s00009-018-1085-0 · Zbl 1394.43002 |
| [8] | Price JF. Inequalities and local uncertainty principles. Journal of Mathematical Physics 1983; 24: 1711-1714. doi: 10.1063/1.525916 · Zbl 0513.60100 |
| [9] | Price JF. Sharp local uncertainty inequalities. Studia Mathematica 1987; 85: 37-45. doi: 10.4064/sm-85-1-37-45 · Zbl 0636.46029 |
| [10] | Rahmouni A. Uncertainty inequalities on Laguerre hpergroup. Mediterranean Journal of Mathematics 2013; 10 (1): 333-351. doi: 10.1007/s00009-012-0198-0 · Zbl 1260.43012 |
| [11] | Rassias JM. On the Heisenberg-Pauli-Weyl inequality. JIPAM. Journal of Inequalities in Pure and Applied Mathematics 2004; 5 (1): Article 4. · Zbl 1057.42007 |
| [12] | Rassias JM. On the Heisenberg-Weyl inequality. JIPAM. Journal of Inequalities in Pure and Applied Mathematics 2005; 6 (1): Article 11. · Zbl 1076.42005 |
| [13] | Rassias JM. On the sharpened Heisenberg-Weyl inequality. JIPAM. Journal of Inequalities in Pure and Applied Mathematics 2006; 7 (3): Article 80. · Zbl 1154.26318 |
| [14] | Rösler M. An uncertainty principle for the Dunkl transform. Bulletin of the Australian Mathematical Society 1999; 59 (3): 353-360. doi: 10.1017/s0004972700033025 · Zbl 0939.33012 |
| [15] | Rösler M, Voit M. An uncertainty principle for Hankel transform. Proceeding of the American Mathematical Society 1999; 127 (1): 183-194. doi: 10.1090/s0002-9939-99-04553-0 · Zbl 0910.44003 |
| [16] | Schwartz L. Topologie générale et analyse fonctionnelle. Paris, France : Hermann, 1970 (in French). · Zbl 0206.06301 |
| [17] | Shimeno N. A note on the uncertainty principle for the Dunkl transform. Journal of Mathematical Sciences (University of Tokyo) 2001; 8 (1): 33-42. · Zbl 0976.33015 |
| [18] | Stein EM. |
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