Time–frequency concentration and localization operators in the Dunkl setting

Baccar, C., Hamadi, N.B., Herch, H.: Time-frequency analysis of localization operators associated to the windowed Hankel transform. Integral Transforms Spec. Funct. 27, 245–258 (2016)

Daubechies, I.: Time-frequency localization operators: a geometric phase space approach. IEEE Trans. Inf. Theory 34, 605–612 (1988)

Dunkl, C.F.: Differential-difference operators associated to reflection groups. Trans. Am. Math. Soc. 311, 16–183 (1989)

Dunkl, C.F.: Integral kernels with reflection group invariance. Can. J. Math. 43, 1213–1227 (1991)

Ghobber, S., Jaming, Ph: Uncertainty principles for integral orperators. Studia Math. 220, 197–220 (2014)

Ghobber, S.: Dunkl-Gabor transform and time-frequency concentration. Czechoslov. Math. J. 65(140), 255–270 (2015)

Ghobber, S.: Shapiro’s uncertainty principle in the Dunkl setting. Bull. Aust. Math. Soc. 92, 98–110 (2015)

Lapointe, L., Vinet, L.: Exact operator solution of the Calogero-Sutherland model. Comm. Math. Phys. 178, 425–452 (1996)

Malinnikova, E.: Orthonormal sequences in $$L^2({\mathbb{R}}^d)$$ L 2 ( R d ) and time frequency localization. J. Fourier Anal. Appl. 16, 983–1006 (2010)

Mejjaoli, H., Sraieb, N.: Uncertainty principles for the continuous Dunkl Gabor transform and the Dunkl continuous wavelet transform. Mediterr. J. Math. 5, 443–466 (2008)

Mejjaoli, H.: Practical inversion formulas for the Dunkl-Gabor transform on $${\mathbb{R}}^d$$ R d . Integral Transforms Spec. Funct. 23, 875–890 (2012)

Polychronakos, A.P.: Exchange operator formalism for integrable systems of particles. Phys. Rev. Lett. 69, 703–705 (1992)

Ramanathan, J., Topiwala, P.: Time-frequency localization via the Weyl correspondence. SIAM J. Math. Anal. 24, 1378–1393 (1993)

Rösler, M.: An uncertainty principle for the Dunkl transform. Bull. Aust. Math. Soc. 59, 353–360 (1999)

Rösler, M., Voit, M.: Markov processes with Dunkl operators. Adv. in Appl. Math. 21, 575–643 (1998)

Shimeno, N.: A note on the uncertainty principle for the Dunkl transform. J. Math. Sci. Univ. Tokyo 8, 33–42 (2001)

Stein, E.M.: Interpolation of linear operators. Trans. Am. Math. Soc. 83, 482–492 (1956)

van Diejen, J.F., Vinet, L.: Calogero-Sutherland-Moser models. CRM Series in Mathematical Physics. Springer-Verlag (2000)

Wong, M.W:. Wavelet transforms and localization operators. Birkhäuser (2002)

Wong, M.W.: Localization operators. Seoul National University Research Institute of Mathematics, Global Analysis Research Center, Seoul (1999)