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Автор: Grafiati

Опубліковано: 6 вересня 2023

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1

McBride, Stephanie, Catherine Fitzgerald, Brian Hand, Michael Cronin, and Mick Wilson. "Uncertainty Principles." Circa, no. 96 (2001): 15. http://dx.doi.org/10.2307/25563696.

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2

Gross, Michael. "Uncertainty principles." Current Biology 19, no. 18 (September 2009): R831—R832. http://dx.doi.org/10.1016/j.cub.2009.09.011.

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3

Jiang, Chunlan, Zhengwei Liu, and Jinsong Wu. "Noncommutative uncertainty principles." Journal of Functional Analysis 270, no. 1 (January 2016): 264–311. http://dx.doi.org/10.1016/j.jfa.2015.08.007.

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4

Hkimi, Siwar, Hatem Mejjaoli, and Slim Omri. "Dispersion’s Uncertainty Principles Associated with the Directional Short-Time Fourier Transform." Studia Scientiarum Mathematicarum Hungarica 57, no. 4 (December 17, 2020): 508–40. http://dx.doi.org/10.1556/012.2020.57.4.1479.

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Анотація:

We introduce the directional short-time Fourier transform for which we prove a new Plancherel’s formula. We also prove for this transform several uncertainty principles as Heisenberg inequalities, logarithmic uncertainty principle, Faris–Price uncertainty principles and Donoho–Stark’s uncertainty principles.

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5

Hleili, Khaled. "A variety of uncertainty principles for the Hankel-Stockwell transform." Open Journal of Mathematical Analysis 5, no. 1 (January 29, 2021): 22–34. http://dx.doi.org/10.30538/psrp-oma2021.0079.

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In this work, we establish \(L^p\) local uncertainty principle for the Hankel-Stockwell transform and we deduce \(L^p\) version of Heisenberg-Pauli-Weyl uncertainty principle. Next, By combining these principles and the techniques of Donoho-Stark we present uncertainty principles of concentration type in the \(L^p\) theory, when \(1< p\leqslant2\). Finally, Pitt's inequality and Beckner's uncertainty principle are proved for this transform.

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6

Bahri, Mawardi, and Ryuichi Ashino. "A Variation on Uncertainty Principle and Logarithmic Uncertainty Principle for Continuous Quaternion Wavelet Transforms." Abstract and Applied Analysis 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/3795120.

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The continuous quaternion wavelet transform (CQWT) is a generalization of the classical continuous wavelet transform within the context of quaternion algebra. First of all, we show that the directional quaternion Fourier transform (QFT) uncertainty principle can be obtained using the component-wise QFT uncertainty principle. Based on this method, the directional QFT uncertainty principle using representation of polar coordinate form is easily derived. We derive a variation on uncertainty principle related to the QFT. We state that the CQWT of a quaternion function can be written in terms of the QFT and obtain a variation on uncertainty principle related to the CQWT. Finally, we apply the extended uncertainty principles and properties of the CQWT to establish logarithmic uncertainty principles related to generalized transform.

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7

Fei, Minggang, Yubin Pan, and Yuan Xu. "Some shaper uncertainty principles for multivector-valued functions." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 06 (November 2016): 1650043. http://dx.doi.org/10.1142/s0219691316500430.

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Анотація:

The Heisenberg uncertainty principle and the uncertainty principle for self-adjoint operators have been known and applied for decades. In this paper, in the framework of Clifford algebra, we establish a stronger Heisenberg–Pauli–Wely type uncertainty principle for the Fourier transform of multivector-valued functions, which generalizes the recent results about uncertainty principles of Clifford–Fourier transform. At the end, we consider another stronger uncertainty principle for the Dunkl transform of multivector-valued functions.

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8

Ghobber, Saifallah, and Hatem Mejjaoli. "Deformed Wavelet Transform and Related Uncertainty Principles." Symmetry 15, no. 3 (March 7, 2023): 675. http://dx.doi.org/10.3390/sym15030675.

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The deformed wavelet transform is a new addition to the class of wavelet transforms that heavily rely on a pair of generalized translation and dilation operators governed by the well-known Dunkl transform. In this study, we adapt the symmetrical properties of the Dunkl Laplacian operator to prove a class of quantitative uncertainty principles associated with the deformed wavelet transform, including Heisenberg’s uncertainty principle, the Benedick–Amrein–Berthier uncertainty principle, and the logarithmic uncertainty inequalities. Moreover, using the symmetry between a square integrable function and its Dunkl transform, we establish certain local-type uncertainty principles involving the mean dispersion theorems for the deformed wavelet transform.

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9

Bhat, Mohammad Younus, Aamir Hamid Dar, Irfan Nurhidayat, and Sandra Pinelas. "Uncertainty Principles for the Two-Sided Quaternion Windowed Quadratic-Phase Fourier Transform." Symmetry 14, no. 12 (December 15, 2022): 2650. http://dx.doi.org/10.3390/sym14122650.

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A recent addition to the class of integral transforms is the quaternion quadratic-phase Fourier transform (Q-QPFT), which generalizes various signal and image processing tools. However, this transform is insufficient for addressing the quadratic-phase spectrum of non-stationary signals in the quaternion domain. To address this problem, we, in this paper, study the (two sided) quaternion windowed quadratic-phase Fourier transform (QWQPFT) and investigate the uncertainty principles associated with the QWQPFT. We first propose the definition of QWQPFT and establish its relation with quaternion Fourier transform (QFT); then, we investigate several properties of QWQPFT which includes inversion and the Plancherel theorem. Moreover, we study different kinds of uncertainty principles for QWQPFT such as Hardy’s uncertainty principle, Beurling’s uncertainty principle, Donoho–Stark’s uncertainty principle, the logarithmic uncertainty principle, the local uncertainty principle, and Pitt’s inequality.

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10

Stark, Hans-Georg, Florian Lieb, and Daniel Lantzberg. "Variance based uncertainty principles and minimum uncertainty samplings." Applied Mathematics Letters 26, no. 2 (February 2013): 189–93. http://dx.doi.org/10.1016/j.aml.2012.08.009.

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11

Blanco-Pérez, Carlos. "On a conceptual connection between the principles of relativity and uncertainty." Physics Essays 32, no. 3 (September 2, 2019): 313–17. http://dx.doi.org/10.4006/0836-1398-32.3.313.

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Анотація:

The principles of relativity and uncertainty represent two of the deepest and most encompassing propositions of the physical sciences. Indeed, much of our present knowledge of nature can be recapitulated in these important statements about the processes of motion and measurement. However, a question remains as to the precise logical connection between both principles. Here, we show a plausible and simple conceptual analysis linking the principles of relativity and uncertainty as logical requirements of the idea of physical measurement. The main conclusion points to the logical complementarity of both principles in order to justify the possibility of physical measurements, in which the uncertainty principle guarantees the applicability of the principle of relativity in all physically conceivable systems of reference.

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12

Ghobber, Saifallah, and Philippe Jaming. "Uncertainty principles for integral operators." Studia Mathematica 220, no. 3 (2014): 197–220. http://dx.doi.org/10.4064/sm220-3-1.

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13

Robert, Christian. "Principles of Uncertainty (Second Edition)." CHANCE 34, no. 1 (January 2, 2021): 54–55. http://dx.doi.org/10.1080/09332480.2021.1885939.

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14

Donoho, David L., and Philip B. Stark. "Uncertainty Principles and Signal Recovery." SIAM Journal on Applied Mathematics 49, no. 3 (June 1989): 906–31. http://dx.doi.org/10.1137/0149053.

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15

Powers, Michael R. "Uncertainty principles in risk finance." Journal of Risk Finance 11, no. 3 (May 25, 2010): 245–48. http://dx.doi.org/10.1108/15265941011043620.

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16

王, 孝通. "Research on Generalized Uncertainty Principles." Advances in Applied Mathematics 05, no. 03 (2016): 421–34. http://dx.doi.org/10.12677/aam.2016.53053.

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17

Wills, Stewart. "Uncertainty Principles: Photonics and Politics." Optics and Photonics News 28, no. 2 (February 1, 2017): 32. http://dx.doi.org/10.1364/opn.28.2.000032.

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18

Lyubarskii, Yurii, and Roman Vershynin. "Uncertainty Principles and Vector Quantization." IEEE Transactions on Information Theory 56, no. 7 (July 2010): 3491–501. http://dx.doi.org/10.1109/tit.2010.2048458.

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19

Li, Zhongkai, and Limin Liu. "Uncertainty principles for Jacobi expansions." Journal of Mathematical Analysis and Applications 286, no. 2 (October 2003): 652–63. http://dx.doi.org/10.1016/s0022-247x(03)00507-9.

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20

Song Goh, Say, and Charles A. Micchelli. "Uncertainty Principles in Hilbert Spaces." Journal of Fourier Analysis and Applications 8, no. 4 (July 1, 2002): 335–74. http://dx.doi.org/10.1007/s00041-002-0017-2.

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21

Okoudjou, Kasso A., and Robert S. Strichartz. "Weak Uncertainty Principles on Fractals." Journal of Fourier Analysis and Applications 11, no. 3 (April 26, 2005): 315–31. http://dx.doi.org/10.1007/s00041-005-4032-y.

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22

Demange, B. "Uncertainty Principles and Light Cones." Journal of Fourier Analysis and Applications 21, no. 6 (March 27, 2015): 1199–250. http://dx.doi.org/10.1007/s00041-015-9401-6.

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23

Strichartz, Robert S. "Uncertainty principles in harmonic analysis." Journal of Functional Analysis 84, no. 1 (May 1989): 97–114. http://dx.doi.org/10.1016/0022-1236(89)90112-2.

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24

Liu, Zhengwei, and Jinsong Wu. "Uncertainty principles for Kac algebras." Journal of Mathematical Physics 58, no. 5 (May 2017): 052102. http://dx.doi.org/10.1063/1.4983755.

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25

Alagic, Gorjan, and Alexander Russell. "Uncertainty principles for compact groups." Illinois Journal of Mathematics 52, no. 4 (December 2008): 1315–24. http://dx.doi.org/10.1215/ijm/1258554365.

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26

Dang, Pei, Chuang Li, Weixiong Mai, and Wenliang Pan. "Uncertainty principles for random signals." Applied Mathematics and Computation 444 (May 2023): 127833. http://dx.doi.org/10.1016/j.amc.2023.127833.

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27

Sitaram, Alladi. "Uncertainty principles and fourier analysis." Resonance 4, no. 2 (February 1999): 20–23. http://dx.doi.org/10.1007/bf02838759.

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28

Costa Filho, Raimundo N., João P. M. Braga, Jorge H. S. Lira, and José S. Andrade. "Extended uncertainty from first principles." Physics Letters B 755 (April 2016): 367–70. http://dx.doi.org/10.1016/j.physletb.2016.02.035.

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29

Jaming, Philippe, and Alexander M. Powell. "Uncertainty principles for orthonormal sequences." Journal of Functional Analysis 243, no. 2 (February 2007): 611–30. http://dx.doi.org/10.1016/j.jfa.2006.09.001.

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30

Meshulam, Roy. "Uncertainty principles and sum complexes." Journal of Algebraic Combinatorics 40, no. 4 (March 21, 2014): 887–902. http://dx.doi.org/10.1007/s10801-014-0512-y.

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31

Goh, Say Song, and Tim N. T. Goodman. "Uncertainty principles and asymptotic behavior." Applied and Computational Harmonic Analysis 16, no. 1 (January 2004): 19–43. http://dx.doi.org/10.1016/j.acha.2003.10.001.

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32

Balila, Edwin A., and Noli N. Reyes. "Weighted Uncertainty Principles in L∞." Journal of Approximation Theory 106, no. 2 (October 2000): 241–48. http://dx.doi.org/10.1006/jath.2000.3494.

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33

Moradpour, H., A. H. Ziaie, S. Ghaffari, and F. Feleppa. "The generalized and extended uncertainty principles and their implications on the Jeans mass." Monthly Notices of the Royal Astronomical Society: Letters 488, no. 1 (June 19, 2019): L69—L74. http://dx.doi.org/10.1093/mnrasl/slz098.

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Анотація:

ABSTRACT The generalized and extended uncertainty principles affect the Newtonian gravity and also the geometry of the thermodynamic phase space. Under the influence of the latter, the energy–temperature relation of ideal gas may change. Moreover, it seems that the Newtonian gravity is modified in the framework of the Rényi entropy formalism motivated by both the long-range nature of gravity and the extended uncertainty principle. Here, the consequences of employing the generalized and extended uncertainty principles, instead of the Heisenberg uncertainty principle, on the Jeans mass are studied. The results of working in the Rényi entropy formalism are also addressed. It is shown that unlike the extended uncertainty principle and the Rényi entropy formalism that lead to the same increase in the Jeans mass, the generalized uncertainty principle can decrease it. The latter means that a cloud with mass smaller than the standard Jeans mass, obtained in the framework of the Newtonian gravity, may also undergo the gravitational collapse process.

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34

Wan, Wen, Bao Zhong Wu, Jing Zhao Yang, Guo Xi Li, and Pei Zhang. "Uncertainty Analysis and Simulation of Coordinate Measuring Definition." Advanced Materials Research 542-543 (June 2012): 735–40. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.735.

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Анотація:

Measurement uncertainty is an important standard for evaluating the measuring results, and have a significant meaning in the engineering application. In this paper, based on the uncertainty assessment principle and the measurement definitions, the source of uncertainty and the influence factors on measurement uncertainty are investigated. Taking straightness as an example, the uncertainty and acceptance limit under different assessment principles are quantitatively calculated, respectively. Moreover, the apply range of different assessment principles based on different uncertainty goals is discussed. Finally, the influence of different definition methods on the mersurement results is demenstrated taking the quantity of the distance between two parallel planes as an example.

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35

N. Safouane, A. Abouleaz, and R. Daher. "Donoho-Stark uncertainty principle for the generalized Bessel transform." Malaya Journal of Matematik 4, no. 03 (July 1, 2016): 513–18. http://dx.doi.org/10.26637/mjm403/022.

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Анотація:

The generalized Bessel transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Donoho-Stark uncertainty principle is obtained for the generalized Bessel transform.

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36

Kawazoe, Takeshi, and Hatem Mejjaoli. "Uncertainty principles for the Dunkl transform." Hiroshima Mathematical Journal 40, no. 2 (July 2010): 241–68. http://dx.doi.org/10.32917/hmj/1280754424.

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37

Amghar, Walid. "Uncertainty Principles for Heisenberg Motion Group." Abstract and Applied Analysis 2021 (November 28, 2021): 1–7. http://dx.doi.org/10.1155/2021/3734817.

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Анотація:

In this article, we will recall the main properties of the Fourier transform on the Heisenberg motion group G = ℍ n ⋊ K , where K = U n and ℍ n = ℂ n × ℝ denote the Heisenberg group. Then, we will present some uncertainty principles associated to this transform as Beurling, Hardy, and Gelfand-Shilov.

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38

KAWAZOE, Takeshi. "Uncertainty Principles for the Jacobi Transform." Tokyo Journal of Mathematics 31, no. 1 (June 2008): 127–46. http://dx.doi.org/10.3836/tjm/1219844827.

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39

Yang, Yan, Pei Dang, and Tao Qian. "Stronger uncertainty principles for hypercomplex signals." Complex Variables and Elliptic Equations 60, no. 12 (May 26, 2015): 1696–711. http://dx.doi.org/10.1080/17476933.2015.1041938.

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40

Pye, J. "Covariant bandlimitation from Generalized Uncertainty Principles." Journal of Physics: Conference Series 1275 (September 2019): 012025. http://dx.doi.org/10.1088/1742-6596/1275/1/012025.

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41

Donoho, D. L., and X. Huo. "Uncertainty principles and ideal atomic decomposition." IEEE Transactions on Information Theory 47, no. 7 (2001): 2845–62. http://dx.doi.org/10.1109/18.959265.

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42

Tuan, Vu Kim. "Uncertainty principles for the Hankel transform." Integral Transforms and Special Functions 18, no. 5 (May 2007): 369–81. http://dx.doi.org/10.1080/10652460701320745.

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43

Reimann, Hans Martin. "Uncertainty principles for the affine group." Functiones et Approximatio Commentarii Mathematici 40, no. 1 (March 2009): 45–67. http://dx.doi.org/10.7169/facm/1238418797.

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44

DEMANGE, BRUNO. "UNCERTAINTY PRINCIPLES FOR THE AMBIGUITY FUNCTION." Journal of the London Mathematical Society 72, no. 03 (December 2005): 717–30. http://dx.doi.org/10.1112/s0024610705006903.

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45

Juan Zhao, Ran Tao, Yan-Lei Li, and Yue Wang. "Uncertainty Principles for Linear Canonical Transform." IEEE Transactions on Signal Processing 57, no. 7 (July 2009): 2856–58. http://dx.doi.org/10.1109/tsp.2009.2020039.

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46

DAHER, R., S. L. HAMAD, T. KAWAZOE, and N. SHIMENO. "Uncertainty principles for the Cherednik transform." Proceedings - Mathematical Sciences 122, no. 3 (August 2012): 429–36. http://dx.doi.org/10.1007/s12044-012-0079-2.

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47

Jaming, Philippe. "Nazarov's uncertainty principles in higher dimension." Journal of Approximation Theory 149, no. 1 (November 2007): 30–41. http://dx.doi.org/10.1016/j.jat.2007.04.005.

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48

Blackorby, Charles, Walter Bossert, and David Donaldson. "Uncertainty and critical-level population principles." Journal of Population Economics 11, no. 1 (March 2, 1998): 1–20. http://dx.doi.org/10.1007/s001480050055.

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49

Sitaram, A., M. Sundari, and S. Thangavelu. "Uncertainty principles on certain Lie groups." Proceedings Mathematical Sciences 105, no. 2 (May 1995): 135–51. http://dx.doi.org/10.1007/bf02880360.

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50

Stollmann, Peter. "From Uncertainty Principles to Wegner Estimates." Mathematical Physics, Analysis and Geometry 13, no. 2 (February 6, 2010): 145–57. http://dx.doi.org/10.1007/s11040-010-9072-0.

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