Abstract
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 \(\mathrm {L}_{Q}^{2}\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abilov, V.A., Abilova, F.V.: Approximation of functions by Fourier-Bessel sums. Izv. Vyssh. Uchebn. Zaved. Mat. 8, 3–9 (2001)
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)
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)
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)
Titchmarsh, E.C.: Introduction of the Theory of Fourier Integrals. Oxford University Press, Oxford (1937)
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professor François Rouvière for his 70’s birthday.
Rights and permissions
About this article
Cite this article
Daher, R., Hamma, M.E. An analog of Titchmarsh’s theorem for the generalized Dunkl transform. J. Pseudo-Differ. Oper. Appl. 7, 59–65 (2016). https://doi.org/10.1007/s11868-015-0130-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11868-015-0130-z