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Research Articles

Integrability of the Fourier–Jacobi transform of functions satisfying Lipschitz and Dini–Lipschitz-type estimates

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Pages 115-126 | Received 22 Aug 2020, Accepted 02 Apr 2021, Published online: 17 Apr 2021

References

  • Sveshnikov AG, Bogolyubov AN, Kravtsov VV. Lecture in mathematical physics. Moscow: Nauka; 2004. Russian.
  • Titchmarsh EC. Eigenfunction expansions associated with second-order differential equations. Moscow: Kom-Kniga; 2005 (Oxford: Clarendon; 1962).
  • Zhukov AI. The Fourier method in computational mathematics. Vol. 6. Moscow: Fizmatlit; 1992. Russian.
  • Titchmarsh EC. Introduction to the theory of Fourier integrals. Oxford: Clarendon Press; 1937.
  • Younis MS. Fourier transforms of Dini-Lipschitz functions. Int J Math Math Sci. 1986;9(2):301–312.
  • Daher R, Tyr O. Weighted approximation for the generalized discrete Fourier-Jacobi transform on space Lp(T). J Pseudo-Differ Oper Appl. 2020;11:1685–1697.
  • Koornwinder TH. Jacobi functions and analysis on noncompact semisimple Lie groups. In: Askey RA, Koornwinder TH, Schempp WJ, editors. Special functions: group theoretical aspects and applications. Dordrecht: D. Reidel Publishing Company; 1984. p. 1–85.
  • Yakubovich SB, Luchko YF. The hypergeometric approach to integral transforms and convolutions. Dordrecht: Kluwer Academic Publishers; 1994.
  • Yakubovich SB. Index transforms. London: World Scientific; 1996.
  • Neretin YF. Index hypergeometric transform and imitation of analysis of Berezin kernels on hyperbolic spaces. Sb Math. 2001;192(3):403–432.
  • Flensted-Jensen M, Koornwinder TH. The convolution structure for Jacobi function expansions. Ark Mat. 1973;11:245–262.
  • Koornwinder TH. A new proof of a Paley-Wiener type theorem for the Jacobi transform. Ark Mat. 1975;13:145–159.
  • Platonov SS. Fourier-Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L2 metric: Jackson's type direct theorems. Integral Transforms Spec Funct. 2019;30(4):264–281.
  • Bray WO, Pinsky MA. Growth properties of Fourier transforms via moduli of continuity. J Funct Anal. 2008;28:2265–2285.
  • Daher R, Tyr O. Equivalence of K-functionals and modulus of smoothness generated by a generalized Jacobi-Dunkl transform on the real line. Rend Circ Mat Palermo II Ser. 2020 [cited 2020 Jun 16]. Available from: https://doi.org/https://doi.org/10.1007/s12215-020-00520-7

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