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Research Article

Paley–Wiener theorem for the Weinstein transform and applications

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Pages 616-628 | Received 19 Sep 2016, Accepted 22 May 2017, Published online: 01 Jun 2017

References

  • Paley R, Wiener N. Fourier transform in the complex domain. Providence (RI): Amer. Math. Soc.; 1934.
  • Stein E, Weiss G. Introduction to Fourier analysis on euclidean spaces. Princeton (NJ): Princeton University Press; 1987.
  • Tuan VK. On the range of the Hankel and extended Hankel transforms. J Math Anal Appl. 1997;209:460–478. doi: 10.1006/jmaa.1997.5351
  • Koornwinder TH. A new proof of a Paley–Wiener theorem for the Jacobi transform. Ark Mat. 1975;13:145–159. doi: 10.1007/BF02386203
  • Tuan VK. New type Paley–Wiener theorems for the modified multidimensional Mellin transform. J Fourier Anal Appl. 1998;4(3):317–328. doi: 10.1007/BF02476030
  • Tuan VK, Zayed AI. Paley–Wiener-type theorems for a class of integral transforms. J Math Anal Appl. 2002;266:200–226. doi: 10.1006/jmaa.2001.7740
  • Lopez AB, Sánchez OL. The Clifford–Fourier transform F0 and monogenic extensions. arXiv:1405.6398v1.
  • Kou K-I, Qian T. Paley–Wiener Theorem In Rn With Clifford Analysis Setting. J Funct Anal. 2002;189:227–241. doi: 10.1006/jfan.2001.3848
  • Ben Nahia Z, Ben Salem N. Spherical harmonics and applications associated with the Weinstein operator. In: Král J, Lukeš J, Netuka I, Veselý J, editors. Potential Theory – ICPT 94: Proceedings of the International Conference on Potential Theory; 1994 Aug 13–20; Kouty, Czec Republic; 1996. p. 235–241.
  • Ben Nahia Z, Ben Salem N. On a mean value property associated with the Weinstein operator. In: Král J, Lukeš J, Netuka I, Veselý J, editors. Potential Theory – ICPT 94: Proceedings of the International Conference on Potential Theory; 1994 Aug 13–20; Kouty, Czec Republic; 1996. p. 243–253.
  • Brelot M. Equation de Weinstein et potentiels de Marcel Riesz. Semin. Theor. Potent. Paris No 3 Lect. Notes Math. 681. 1979. p. 18–38.
  • Mehrez K. Weinstein positive definite functions (accepted in Positivity). Forthcoming.
  • Mejjaoli H, Salhi M. Uncertainty principles for the Weinstein transform. Czechoslovak Math J. 2011;61(4):941–974. doi: 10.1007/s10587-011-0061-7
  • Debnath L. Integral transform and their applications. Boca Raton (FL): CRC Press, Inc.; 1995.
  • Moumni T, Zayed AI. A generalization of the prolate spheroidal wave functions with applications to sampling. Integral Transforms Spec Funct. 2014;25(6):433–447. doi: 10.1080/10652469.2013.873426

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