Hardy’s and Miyachi’s Theorems for the First Hankel–Clifford Transform
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We present an analog of Hardy’s and Miyachi’s theorems for the first Hankel–Clifford transform.
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References
- 1.V. A. Abilov and F. V. Abilova, “Approximation of functions by Fourier–Bessel sums,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 8, 3–9 (2001).Google Scholar
- 2.J. J. Betancor, “The Hankel–Clifford transformation on certain spaces of ultradistributions,” Indian J. Pure Appl. Math., 20, No. 6, 583–603 (1989).MathSciNetzbMATHGoogle Scholar
- 3.M. Cowling and J. Price, “Generalizations of Heisenberg’s inequality,” Harmon. Anal.: Lect. Notes Math., Springer, Berlin, 992 (1983).Google Scholar
- 4.M. El Kassimi, “An L p− L q version of Morgan’s and Cowling–Price’s theorem for the first Hankel–Clifford transform,” Nonlin. Stud., 26, No. 1 (2019).Google Scholar
- 5.A. Gray, G. B. Matthews, and T. M. Macrobert, A Treatise on Bessel Functions and Their Applications to Physics, MacMillan, London (1952).Google Scholar
- 6.G. H. Hardy, “A theorem concerning Fourier transforms,” J. Lond. Math. Soc. (2), 8, 227–231 (1933).MathSciNetCrossRefGoogle Scholar
- 7.V. Havin and B. Jöricke, “The uncertainty principle in harmonic analysis,” Ser. Modern Surv. Math., 28 (1994).Google Scholar
- 8.N. N. Lebedev, Special Functions and Their Applications, Dover Publ., New York (1972).zbMATHGoogle Scholar
- 9.J. M. R. M’endez P’erez and M. M. Socas Robayna, “A pair of generalized Hankel–Clifford transformations and their applications,” J. Math. Anal. Appl., 154, No. 2, 543–557 (1991).MathSciNetCrossRefGoogle Scholar
- 10.S. P. Malgonde and S. R. Bandewar, “On the generalized Hankel–Clifford transformation of arbitrary order,” Proc. Indian Acad. Sci. Math. Sci., 110, No. 3, 293–304 (2000).MathSciNetCrossRefGoogle Scholar
- 11.A. Miyachi, “A generalization of the theorem of Hardy,” in: Harmon. Analysis. Semin. Izunagaoka, Shizuoka-Ken, Japan (1997), pp. 44–51.Google Scholar
- 12.A. Prasad, V. K. Singh, and M. M. Dixit, “Pseudo-differential operators involving Hankel–Clifford transformation,” Asian-Eur. J. Math., 5, No. 3, 1250040, 15 p. (2012).MathSciNetCrossRefGoogle Scholar
- 13.A. Sitaram and M. Sundari, “An analog of Hardy’s theorem for very rapidly decreasing functions on semisimple Lie groups,” Pacific J. Math., 177, 187–200 (1997).MathSciNetCrossRefGoogle Scholar
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