Time-frequency analysis associated with the k-Hankel wavelet transform on ℝ^d

References

• Ben Saïd S, Kobayashi T, Ørsted B. Laguerre semigroup and Dunkl operators. Compos Math. 2012;148(4):1265–1336.
   Web of Science ®Google Scholar
• Dunkl CF. Differential-difference operators associated to reflection groups. Trans Am Math Soc. 1989;311:167–183.
   Web of Science ®Google Scholar
• Dunkl CF. Hankel transforms associated to finite reflection groups. In: Proceedings of the Special Session on Hypergeometric Functions on Domains of Positivity, Jack Polynomials and Applications. Vol. 138; Tampa, FL; 1991. Contemporary Mathematics. 1992. p. 123–138.
   Google Scholar
• Howe R. The oscillator semigroup. In: The mathematical heritage of Hermann Weyl (Durham, NC, 1987). Providence, RI: American Mathematical Society; 1988. p. 61–132. (Proceedings of symposia in pure mathematics; 48).
   Google Scholar
• Kobayashi T, Mano G. The Schrödinger model for the minimal representation of the indefinite orthogonal group O(p,q). Mem Am Math Soc. 2011;212(1000):vi + 132pp.
   Google Scholar
• Ben Saïd S. A product formula and a convolution structure for a k-Hankel transform on R. J Math Anal Appl. 2018;463(2):1132–1146.
   Web of Science ®Google Scholar
• Ben Saïd S, Deleaval L. Translation operator and maximal function for the (k,1)-generalized Fourier transform. J Funct Anal. 2020;279(8):108706. doi:10.1016/j.jfa.2020.108706
   Web of Science ®Google Scholar
• Constales D, De Bie H, Lian P. Explicit formulas for the Dunkl dihedral kernel and the (κ,a)-generalized Fourier kernel. J Math Anal Appl. 2018;460(2):900–926.
   Web of Science ®Google Scholar
• Gorbachev D, Ivanov V, Tikhonov S. Pitt's inequalities and uncertainty principle for generalized Fourier transform. Int Math Res Notices. 2016;2016(23):7179–7200.
   Web of Science ®Google Scholar
• Johansen TR. Weighted inequalities and uncertainty principles for the (k,a)-generalized Fourier transform. Int J Math. 2016;27(3):1650019.
   Web of Science ®Google Scholar
• Mejjaoli H. Wavelet-multipliers analysis in the framework of the k-Laguerre theory. Linear Multilinear Algebra. 2017;67(1):1–24.
   Web of Science ®Google Scholar
• Mejjaoli H. Spectral theorems associated with the (k,a)-generalized wavelet multipliers. J Pseudo-Differ Oper Appl. 2018;9:735–762.
   Web of Science ®Google Scholar
• Mejjaoli H. (k,a)-generalized wavelet transform and applications. J Pseudo-Differ Oper Appl. 2020;11:55–92.
   Web of Science ®Google Scholar
• Daubechies I. Time-frequency localization operators: a geometric phase space approach. IEEE Trans Inf Theory. 1988;34(4):605–612.
   Web of Science ®Google Scholar
• Boggiatto P, Wong MW. Two-wavelet localization operators on Lp(Rd) for the Weyl-Heisenberg group. Integral Equ Oper Theory. 2004;49:1–10.
   Web of Science ®Google Scholar
• Wong MW. Localization operators on the Weyl-Heisenberg group. In: Pathak RS, editor. Geometry, analysis and applications. World-Scientific; 2001. p. 303–314.
   Google Scholar
• Wong MW. Lp boundedness of localization operators associated to left regular representations. Proc Am Math Soc. 2002;130(10):2911–2919.
   Web of Science ®Google Scholar
• Wong MW. Localization operators on the affine group and paracommutators. In Progress in analysis. World Scientific; 2003. p. 663–669.
   Google Scholar
• Wong MW. Wavelet transforms and localization operators, operator theory: Advances and applications. Basel: Birkhäuser; 2002.136.
   Google Scholar
• Balazs P. Hilbert–Schmidt operators and frames-classification, best approximation by multipliers and algorithms. Int J Wavelets Multiresolution Inf Process. 2008;6(2):315–330.
   Web of Science ®Google Scholar
• Cordero E, Gröchenig K. Time–frequency analysis of localization operators. J Funct Anal. 2003;205(1):107–131.
   Web of Science ®Google Scholar
• De Mari F, Feichtinger H, Nowak K. Uniform eigenvalue estimates for time-frequency localization operators. J London Math Soc. 2002;65(3):720–732.
   Google Scholar
• Gröchenig K. Foundations of time-frequency analysis. Boston, MA: Birkhäuser Boston, Inc.; 2001. (Applied and numerical harmonic analysis).
   Google Scholar
• Addison PS, Watson JN, Clegg GR, et al. Finding coordinated atrial activity during ventricular fibrillation using wavelet decomposition. IEEE Trans Eng Med Biol. 2002;21:58–65.
   PubMedGoogle Scholar
• Sukiennik P, Bialasiewicz JT. Cross-correlation of bio-signals using continuous wavelet transform and genetic algorithm. J Neurosci Meth. 2015;247:13–22.
   PubMed Web of Science ®Google Scholar
• Rösler M. Positivity of Dunkl's intertwining operator. Duke Math J. 1999;98:445–463.
   Web of Science ®Google Scholar
• Abreu LD, Gröchenig K, Romero JL. On accumulated spectrograms. Trans Am Math Soc. 2016;368:3629–3649.
   Web of Science ®Google Scholar
• Riesz F, Nagy BS. Functional analysis. New York: Frederick Ungar Publishing Co.; 1995.
   Google Scholar