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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).

  2. J. J. Betancor, “The Hankel–Clifford transformation on certain spaces of ultradistributions,” Indian J. Pure Appl. Math., 20, No. 6, 583–603 (1989).

    MathSciNet  MATH  Google Scholar 

  3. M. Cowling and J. Price, “Generalizations of Heisenberg’s inequality,” Harmon. Anal.: Lect. Notes Math., Springer, Berlin, 992 (1983).

  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).

  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).

    Article  MathSciNet  Google Scholar 

  7. V. Havin and B. Jöricke, “The uncertainty principle in harmonic analysis,” Ser. Modern Surv. Math., 28 (1994).

  8. N. N. Lebedev, Special Functions and Their Applications, Dover Publ., New York (1972).

    MATH  Google 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).

    Article  MathSciNet  Google 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).

    Article  MathSciNet  Google Scholar 

  11. A. Miyachi, “A generalization of the theorem of Hardy,” in: Harmon. Analysis. Semin. Izunagaoka, Shizuoka-Ken, Japan (1997), pp. 44–51.

  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).

    Article  MathSciNet  Google 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).

    Article  MathSciNet  Google Scholar 

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Correspondence to M. El Kassimi.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 5, pp. 710–715, May, 2019

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El Kassimi, M., Fahlaoui, S. Hardy’s and Miyachi’s Theorems for the First Hankel–Clifford Transform. Ukr Math J 71, 812–818 (2019). https://doi.org/10.1007/s11253-019-01679-8

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  • DOI: https://doi.org/10.1007/s11253-019-01679-8

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