Editor in Chief - Anry Nersessian (Institute of Mathematics NAS, Armenia)
Deputy Editor - Rafayel Barkhudaryan (Institute of Mathematics NAS, Armenia)
Managing Editor - Linda Khachatryan (Institute of Mathematics NAS, Armenia)
e-mail: ajm@instmath.sci.am
According to the latest Scimago Journal Rank, Armenian Journal of Mathematics has maintained its position in Q3 with an SJR score of 0.36.
Read more about Armenian Journal of Mathematics has been recognized as a Q3 journal in SJRThe Sturm-Liouville wavelet transform (SLWT) is a novel addition to the class of Sturm-Liouville transforms, which has gained a respectable status in the realm of time-frequency signal analysis within a short span of time. Given that the study of time-frequency analysis is of both theoretically interesting and practically useful, the aim of this paper is to explore a class of quantitative uncertainty principles (UP) associated with SLWT, including Faris local-type UP, Shannon-type UP, Donoho-Stark-type UP and Benedicks-type UP.
L.B. Attour and K. Trim`eche, Uncertainty principle and $(L^p,L^q)$ sufficient pairs on Chébli-Trimèche hypergroups. Integral Transform. Spec. Funct., 16 (2005), no. 8, pp. 625-637.
C. Baccar, Uncertainty principles for the continuous Hankel wavelet transform. Integral Transform. Spec. Funct., 27 (2016), no. 6, pp. 413-429.
W. R. Bloom and Z. Xu, Fourier multipliers for $L^p$ on Chébli-Trimèche hypergroups. Proc. London Math. Soc., 80 (2000), no. 03, pp. 643-664.
H. Chébli, Théorème de Paley-Wiener associé à un opérateur différentiel singulier sur $(0,∞)$. J. Math. Pures Appl., 58 (1979), no. 1, pp. 1-19.
R. Daher, T. Kawazoe and H. Mejjaoli, A generalization of Miyachi's theorem. J. Math. Soc. Japan, 61 (2009), no. 2, pp. 551-558.
I. Daubechies, Ten lectures on wavelets, Vol. 61. Siam, 1992.
L. Debnath and D. Bhatta, Integral transforms and their applications, Third Edition, Chapman and Hall, CRC Press, Boca Raton, Florida, 2015.
D. L. Donoho and P. B. Stark, Uncertainty principles and signal recovery. SIAM J. Appl. Math., 49 (1989), no. 3, pp. 906-931.
M. Flensted-Jensen and T. Koornwinder, The convolution structure for Jacobi function expansions. Ark. Mat., 11 (1973), no. 1-2, pp. 245-262.
D. Gabor, Theory of communication, Part 1: The analysis of information. J. Inst. Electr. Eng., 93 (1946), no. 26, pp. 429-441.
A. Grossmann and J. Morlet, Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM J. Math. Anal., 15 (1984), no. 4, pp. 723-736.
N. B. Hamadi, Z. Hafirassou and H. Herch, Uncertainty principles for the Hankel-Stockwell transform. J. Pseudo-Differ. Oper. Appl., 11 (2020), no. 2, pp. 543-564.
N. B. Hamadi and S. Omri, Uncertainty principles for the continuous wavelet transform in the Hankel setting. Appl. Anal., 97 (2018), no. 4, pp. 513-527.
V. Havin and B. Jöricke, The uncertainty principle in harmonic analysis, Ergebnisse der Mathematik und ihrer Grenzgebiete 3, Folge. 28, Springer, Berlin, 1994.
S. Hkimi and S. Omri, Uncertainty principles in term of supports in Hankel wavelet setting. Oper. Matrices, 15 (2021), no. 2, pp. 755-776.
R. Ma, Heisenberg uncertainty principle on Chèbli-Triméche hypergroups. Pacific J. Math., 235 (2008), no. 2, pp. 289-296.
J. Maan and E. R. Negrín, Parseval--Goldstein type theorems for integral transforms in a general setting. Istanbul J. Math., 2 (2024), no. 1, pp. 33-38.
J. Maan and E. R. Negrín, Parseval-Goldstein type theorems for the index Whittaker transform. Integral Transform. Spec. Funct., 36 (2025), no. 1, pp. 53-63.
J. Maan and A. Prasad, A pair of pseudo-differential operators involving index Whittaker transform in $L^a_2(R_+; m_a(x) dx)$. Acta. Math. Sin.-English Ser., 40 (2024), no. 6, pp. 1420-1430.
M. A. Mourou and K. Trimèche, Calderón's reproducing formula for a singular differential operator and inversion of the generalized Abel transform. J. Fourier Anal. Appl. 4 (1998), no. 2, pp. 229-245.
E. R. Negrín, B. J. González and J. Maan, Parseval-Goldstein-type theorems for Lebedev-Skalskaya transforms. Axioms, 13 (2024), no. 9, Art. 630.
E. R. Negrín and J. Maan, On $L^p$-Boundedness properties and Parseval-Goldstein-type theorems for a Lebedev-type index transform. Mathematics, 12 (2024), no. 24, Art. 3907.
S. S. Platonov, Fourier-Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in $L_2$ metric: Nikol'ski-Besov type functions spaces. Integral Transform. Spec. Funct., 1 (2020), no. 4, pp. 281-298.
F. A. Shah and A. Y. Tantary, Wavelet transforms: Kith and Kin, Chapman and Hall/CRC, Boca Raton, 2022.
C. E. Shannon, A mathematical theory of communication. ACM SIGMOBILE Mobile Computing and Communications Review, 5 (2001), no. 1, pp. 3-55.
F. Soltani, $L^p$ local uncertainty inequality for the Sturm-Liouville transform. CUBO A Math. J., 16 (2014), no. 1, pp. 95-104.
F. Soltani, Donoho-Stark uncertainty principle associated with a singular second-order differential operator. Int. J. Anal. Appl., 4 (2014), no. 1, pp. 1-10.
F. Soltani, Parseval-Goldstein type theorems for the Sturm-Liouville transform. Integral Transform. Spec. Funct., 36 (2025), no. 8, pp. 634-646.
F. Soltani and M. Aloui, Lipschitz and Dini-Lipschitz functions for the Sturm--Liouville transform. Integral Transform. Spec. Funct., 35 (2024), no. 11, pp. 612-625.
F. Soltani and M. Aloui, Hausdorff operators associated with the Sturm-Liouville operator. Rend. Circ. Mat. Palermo, II. Ser., 74 (2025), no. 1, Art. 54.
F. Soltani and Y. Zarrougui, Reconstruction and best approximate inversion formulas for the
Sturm--Liouville-Stockwell transform. Appl. Math. E-Notes, 25 (2025), pp. 57-72.
F. Soltani and Y. Zarrougui, Localization operators and Shapiro's inequality for the Sturm-Liouville-Stockwell transform. J. Math. Sci., 289 (2025), no. 1, pp. 45-58.
F. Soltani and Y. Zarrougui, Toeplitz operators and spectrogram associated with the Sturm-Liouville-Stockwell transform. Filomat, 39 (2025), no. 18, pp. 6295-6310.
F. Soltani and Y. Zarrougui, Quantitative uncertainty principles associated with the Sturm-Liouville-Stockwell transform. Novi Sad J. Math., (2026), (to appear).
M. Stephane, A wavelet tour of signal processing, The Sparse Way, 1999.
K. Trimèche, Transformation intégrale de Weyl et théorème de Paley-Wiener associés à un opérateur différentiel singulier sur $(0,∞)$. J. Math. Pures Appl., 60 (1981), no. 1, pp. 51-98.
K. Trimèche, Inversion of Lions transmutation operators using generalized wavelets. Appl. Comput. Harmonic Anal., 4 (1997), no. 1, pp. 97-112.
E. Wilczok, New uncertainty principles for the continuous Gabor transform and the continuous Wavelet transform. Doc. Math., 5 (2000), pp. 207-226.
H. Zeuner, The central limit theorem for Chébli-Trimèche hypergroups. J. Theor. Proba., 2 (1989), no. 1, pp. 51-63.
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