Uncertainty Principles for the Dunkl-Bessel type transform
Keywords:Beurling’s theorem, Gelfand-Shilov theorem, Cowling-Price’s theorem, Morgan’s theorem
The Dunkl-Bessel type transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Beurling’s theorem, Gelfand-Shilov theorem, Cowling-Price’s theorem and Morgan’s theorem are obtained for the Dunkl-Bessel type transform.
A. Abouelaz, A. Achak, R. Daher, El. Loualid, Harmonic analysis associated with the Dunkl-Bessel type-Laplace operator, (IJAREM) volume. 01, Issue 04, July 2015.
A. Beurling, In: The Collected Works of Arne Beurling. Birkhäuser, Boston (1989), 1-2.
A. Bonami, B. Demange and P. Jaming, Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms. Rev. Mat. Iberoamericana 19 (2002), 22-35.
L. Bouattour and K. Trimèche, An analogue of Beurling-Hörmader’s theorem for the Chébli-Trimèche transfrom. Global J. of Pure and Appl. Math. 1, No 3(2005), 342-357.
M. G. Cowling and J. F. Prices, Generalizations of Heisemberg’s inequality. In: Lecture Notes in Math. 992, Springer, Berlin (1983), 443-449.
G. H. Hardy, A theorem concerning Fourier transform. J. London Math. Soc. 8 (1933), 227-231.
L. Hörmander, A uniqueness theorem of Beurling for Fourier transform pairs. Ark.F?or Math. 2, No 2 (1991), 237-240.
H. Mejjaoli and K. Trimèche, An analogue of Hardy’s theorem and its Lp- version for the Dunkl-Bessel transform. Concrete Mathematica (2004).
G. W. Morgan, A note on Fourier transforms. J. London Math. Soc. 9 (1934), 188-192.
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