A new class of uncertainty principles for the k-Hankel wavelet transform

References

[1] W. Beckner, Pitt’s inequality and the uncertainty principle, Proc. Amer. Math. Soc. 123 (1995), no. 6, 1897–1905. 10.1090/S0002-9939-1995-1254832-9Suche in Google Scholar

[2] S. Ben Saïd and L. Deleaval, Translation operator and maximal function for the (k,1)-generalized Fourier transform, J. Funct. Anal. 279 (2020), no. 8, Article ID 108706. 10.1016/j.jfa.2020.108706Suche in Google Scholar

[3] S. Ben Saïd, T. Kobayashi and B. Ørsted, Laguerre semigroup and Dunkl operators, Compos. Math. 148 (2012), no. 4, 1265–1336. 10.1112/S0010437X11007445Suche in Google Scholar

[4] M. Benedicks, On Fourier transforms of functions supported on sets of finite Lebesgue measure, J. Math. Anal. Appl. 106 (1985), no. 1, 180–183. 10.1016/0022-247X(85)90140-4Suche in Google Scholar

[5] L. Debnath and F. A. Shah, Wavelet Transforms and Their Applications, 2nd ed., Birkhäuser/Springer, New York, 2015. 10.1007/978-0-8176-8418-1Suche in Google Scholar

[6] L. Debnath and F. A. Shah, Lecture Notes on Wavelet Transforms, Compact Textb. Math., Birkhäuser/Springer, Cham, 2017. 10.1007/978-3-319-59433-0Suche in Google Scholar

[7] C. F. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc. 311 (1989), no. 1, 167–183. 10.1090/S0002-9947-1989-0951883-8Suche in Google Scholar

[8] G. B. Folland and A. Sitaram, The uncertainty principle: A mathematical survey, J. Fourier Anal. Appl. 3 (1997), no. 3, 207–238. 10.1007/BF02649110Suche in Google Scholar

[9] S. Ghobber and P. Jaming, Uncertainty principles for integral operators, Studia Math. 220 (2014), no. 3, 197–220. 10.4064/sm220-3-1Suche in Google Scholar

[10] D. V. Gorbachev, V. I. Ivanov and S. Y. Tikhonov, Pitt’s inequalities and uncertainty principle for generalized Fourier transform, Int. Math. Res. Not. IMRN 2016 (2016), no. 23, 7179–7200. 10.1093/imrn/rnv398Suche in Google Scholar

[11] V. P. Havin and B. Jöricke, The Uncertainty Principle in Harmonic Analysis, Springer, Berlin, 1994. 10.1007/978-3-642-78377-7Suche in Google Scholar

[12] T. R. Johansen, Weighted inequalities and uncertainty principles for the ( k , a ) -generalized Fourier transform, Internat. J. Math. 27 (2016), no. 3, Article ID 1650019. 10.1142/S0129167X16500191Suche in Google Scholar

[13] E. Malinnikova, Orthonormal sequences in L 2 ⁢ ( 𝐑 d ) and time frequency localization, J. Fourier Anal. Appl. 16 (2010), no. 6, 983–1006. 10.1007/s00041-009-9114-9Suche in Google Scholar

[14] H. Mejjaoli, Spectral theorems associated with the ( k , a ) -generalized wavelet multipliers, J. Pseudo-Differ. Oper. Appl. 9 (2018), no. 4, 735–762. 10.1007/s11868-018-0260-1Suche in Google Scholar

[15] H. Mejjaoli, New results for the Hankel two-wavelet multipliers, J. Taibah Univ. Sci. 13 (2019), 32–40. 10.1080/16583655.2018.1521711Suche in Google Scholar

[16] H. Mejjaoli, ( k , a ) -generalized wavelet transform and applications, J. Pseudo-Differ. Oper. Appl. 11 (2020), no. 1, 55–92. 10.1007/s11868-019-00291-5Suche in Google Scholar

[17] H. Mejjaoli, Time-frequency analysis associated with the k-Hankel Gabor transform on ℝ d , J. Pseudo-Differ. Oper. Appl. 12 (2021), no. 3, Paper No. 41. 10.1007/s11868-021-00399-7Suche in Google Scholar

[18] H. Mejjaoli, New uncertainty principles for the ( k , a ) -generalized wavelet transform, Rev. Un. Mat. Argentina 63 (2022), no. 1, 239–279. 10.33044/revuma.2051Suche in Google Scholar

[19] H. Mejjaoli and F. A. Shah, Uncertainty principles associated with the directional short-time Fourier transform, J. Math. Phys. 62 (2021), no. 6, Paper No. 063511. 10.1063/5.0046426Suche in Google Scholar

[20] H. Mejjaoli and N. Sraieb, Uncertainty principles for the continuous Dunkl Gabor transform and the Dunkl continuous wavelet transform, Mediterr. J. Math. 5 (2008), no. 4, 443–466. 10.1007/s00009-008-0161-2Suche in Google Scholar

[21] H. Mejjaoli and K. Trimèche, k-Hankel two-wavelet theory and localization operators, Integral Transforms Spec. Funct. 31 (2020), no. 8, 620–644. 10.1080/10652469.2020.1723011Suche in Google Scholar

[22] M. Rösler, Positivity of Dunkl’s intertwining operator, Duke Math. J. 98 (1999), no. 3, 445–463. 10.1215/S0012-7094-99-09813-7Suche in Google Scholar

[23] S. Saitoh, Integral Transforms, Reproducing Kernels and Their Applications, Pitman Res. Notes Math. Ser. 369, Longman, Harlow, 1997. Suche in Google Scholar

[24] F. A. Shah, K. S. Nisar, W. Z. Lone and A. Y. Tantary, Uncertainty principles for the quadratic-phase Fourier transform, Math. Methods Appl. Sci. 44 (2021), no. 13, 10416–10431. 10.1002/mma.7417Suche in Google Scholar

[25] K. Trimèche, Generalized Wavelets and Hypergroups, Gordon and Breach Science, Amsterdam, 1997. Suche in Google Scholar

[26] M. W. Wong, Wavelet Transforms and Localization Operators, Oper. Theory Adv. Appl. 136, Birkhäuser, Basel, 2002. 10.1007/978-3-0348-8217-0Suche in Google Scholar