An analog of Titchmarsh's theorem for the generalized Dunkl transform

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• 作者：Radouan Daher…
• 关键词：Generalized Dunkl transform ; Differential ; difference operator ; Generalized dual translation operator
• 刊名：Journal of Pseudo-Differential Operators and Applications
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：7
• 期：1
• 页码：59-65
• 全文大小：372 KB
• 参考文献：1.Abilov, V.A., Abilova, F.V.: Approximation of functions by Fourier-Bessel sums. Izv. Vyssh. Uchebn. Zaved. Mat. 8, 3–9 (2001)MathSciNet
  2.Al Zahrani, R.F., Mourou, M.A.: The continuous wavelet transform associated with a Dunkl type operator on the real line. Adv. Pure Math. 3, 443–450 (2013)CrossRef
  3.Al Zahran, R.F., El Mir, H., Mourou, M.A.: Intertwining operators associated with a Dunkl type operator on the real line and applications. Far East J. Appl. Math. Appl. 64(2), 129–144 (2012)
  4.Belkina, E.S., Platonov, S.S.: Equivalence of \(K\) -functionals and modulus of smoothness contructed by generalized Dunkl translations. Izv. Vyss. Ucheb. Zaved. Math. 52(8), 3–15 (2008)
  5.Titchmarsh, E.C.: Introduction of the Theory of Fourier Integrals. Oxford University Press, Oxford (1937)
  
• 作者单位：Radouan Daher (1)
  Mohamed El Hamma (1)
  
  1. Department of Mathematics, Faculty of Sciences Aïn Chock, University of Hassan II, Casablanca, Morocco
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：None Assigned
• 出版者：Birkh盲user Basel
• ISSN：1662-999X

文摘

Using a generalized dual translation operator, we obtain an analog of Titchmarsh’s theorem for the generalized Dunkl transform for functions satisfying the Q-Dunkl Lipschitz condition in the space \(\mathrm {L}_{Q}^{2}\).