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Academic literature on the topic 'Beckner inequality'

Author: Grafiati

Published: 1 April 2023

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Journal articles on the topic "Beckner inequality"

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Kondratyev, Stanislav, Léonard Monsaingeon, and Dmitry Vorotnikov. "A new multicomponent Poincaré–Beckner inequality." Journal of Functional Analysis 272, no. 8 (April 2017): 3281–310. http://dx.doi.org/10.1016/j.jfa.2016.12.018.

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2

Deng, Pingji, and Fengyu Wang. "Beckner Inequality on Finite- and Infinite-Dimensional Manifolds*." Chinese Annals of Mathematics, Series B 27, no. 5 (October 2006): 581–94. http://dx.doi.org/10.1007/s11401-004-0317-8.

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3

AMRI, BESMA, and LAKHDAR T. RACHDI. "BECKNER LOGARITHMIC UNCERTAINTY PRINCIPLE FOR THE RIEMANN–LIOUVILLE OPERATOR." International Journal of Mathematics 24, no. 09 (August 2013): 1350070. http://dx.doi.org/10.1142/s0129167x13500705.

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First, we establish the Stein–Weiss inequality for the B-Riesz potential generated by the Riemann–Liouville operator. Next, we prove the Pitt's and Beckner logarithmic inequalities related to the connected Fourier transform.

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4

Kim, Meelae. "Linearised Moser-Trudinger inequality." Bulletin of the Australian Mathematical Society 62, no. 3 (December 2000): 445–57. http://dx.doi.org/10.1017/s0004972700018967.

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As a limiting case of the Sobolev imbedding theorem, the Moser-Trudinger inequality was obtained for functions in with resulting exponential class integrability. Here we prove this inequality again and at the same time get sharper information for the bound. We also generalise the Linearised Moser inequality to higher dimensions, which was first introduced by Beckner for functions on the unit disc. Both of our results are obtained by using the method of Carleson and Chang. The last section introduces an analogue of each inequality for the Laplacian instead of the gradient under some restricted conditions.

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5

Yao, Nian, and Zhengliang Zhang. "Beckner inequalities for Moebius measures on spheres." ESAIM: Probability and Statistics 23 (2019): 552–66. http://dx.doi.org/10.1051/ps/2018025.

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In this paper, we consider the Moebius measures μxn indexed by dimension n and |x| < 1 on the unit sphere Sn−1 in ℝn (n ≥ 3), and provide a precise two-sided estimate on the order of the Beckner inequality constant with exponent p ∈ [1, 2) in the three parameters. As special cases for p = 1 and p tending to 2, our results cover those in Barthe et al. [Forum Math. (submitted for publication)] for n ≥ 3 and explore an interesting phenomenon.

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Da Pelo, Paolo, Alberto Lanconelli, and Aurel I. Stan. "A sharp interpolation between the Hölder and Gaussian Young inequalities." Infinite Dimensional Analysis, Quantum Probability and Related Topics 19, no. 01 (March 2016): 1650001. http://dx.doi.org/10.1142/s0219025716500016.

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We prove a very general sharp inequality of the Hölder–Young-type for functions defined on infinite dimensional Gaussian spaces. We begin by considering a family of commutative products for functions which interpolates between the pointwise and Wick products; this family arises naturally in the context of stochastic differential equations, through Wong–Zakai-type approximation theorems, and plays a key role in some generalizations of the Beckner-type Poincaré inequality. We then obtain a crucial integral representation for that family of products which is employed, together with a generalization of the classic Young inequality due to Lieb, to prove our main theorem. We stress that our main inequality contains as particular cases the Hölder inequality and Nelson’s hyper-contractive estimate, thus providing a unified framework for two fundamental results of the Gaussian analysis.

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7

Cazacu, Cristian. "A new proof of the Hardy–Rellich inequality in any dimension." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 6 (August 19, 2019): 2894–904. http://dx.doi.org/10.1017/prm.2019.50.

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The Hardy-Rellich inequality in the whole space with the best constant was firstly proved by Tertikas and Zographopoulos in Adv. Math. (2007) in higher dimensions N ⩾ 5. Then it was extended to lower dimensions N ∈ {3, 4} by Beckner in Forum Math. (2008) and Ghoussoub-Moradifam in Math. Ann. (2011) by applying totally different techniques.In this note, we refine the method implemented by Tertikas and Zographopoulos, based on spherical harmonics decomposition, to give an easy and compact proof of the optimal Hardy–Rellich inequality in any dimension N ⩾ 3. In addition, we provide minimizing sequences which were not explicitly mentioned in the quoted papers in lower dimensions N ∈ {3, 4}, emphasizing their symmetry breaking. We also show that the best constant is not attained in the proper functional space.

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8

Santana-Carrillo, R., Jesus S. González-Flores, Emilio Magaña-Espinal, Luis F. Quezada, Guo-Hua Sun, and Shi-Hai Dong. "Quantum Information Entropy of Hyperbolic Potentials in Fractional Schrödinger Equation." Entropy 24, no. 11 (October 24, 2022): 1516. http://dx.doi.org/10.3390/e24111516.

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In this work we have studied the Shannon information entropy for two hyperbolic single-well potentials in the fractional Schrödinger equation (the fractional derivative number (0<n≤2) by calculating position and momentum entropy. We find that the wave function will move towards the origin as the fractional derivative number n decreases and the position entropy density becomes more severely localized in more fractional system, i.e., for smaller values of n, but the momentum probability density becomes more delocalized. And then we study the Beckner Bialynicki-Birula–Mycieslki (BBM) inequality and notice that the Shannon entropies still satisfy this inequality for different depth u even though this inequality decreases (or increases) gradually as the depth u of the hyperbolic potential U1 (or U2) increases. Finally, we also carry out the Fisher entropy and observe that the Fisher entropy increases as the depth u of the potential wells increases, while the fractional derivative number n decreases.

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Mossel, Elchanan, Ryan O'Donnell, Oded Regev, Jeffrey E. Steif, and Benny Sudakov. "Non-interactive correlation distillation, inhomogeneous Markov chains, and the reverse Bonami-Beckner inequality." Israel Journal of Mathematics 154, no. 1 (December 2006): 299–336. http://dx.doi.org/10.1007/bf02773611.

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10

Pedram, Pouria. "The Minimal Length and the Shannon Entropic Uncertainty Relation." Advances in High Energy Physics 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/5101389.

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In the framework of the generalized uncertainty principle, the position and momentum operators obey the modified commutation relationX,P=iħ1+βP2, whereβis the deformation parameter. Since the validity of the uncertainty relation for the Shannon entropies proposed by Beckner, Bialynicki-Birula, and Mycielski (BBM) depends on both the algebra and the used representation, we show that using the formally self-adjoint representation, that is,X=xandP=tan⁡βp/β, where[x,p]=iħ, the BBM inequality is still valid in the formSx+Sp≥1+ln⁡πas well as in ordinary quantum mechanics. We explicitly indicate this result for the harmonic oscillator in the presence of the minimal length.

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Books on the topic "Beckner inequality"

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Church, Tom (Research fellow), editor, Miller, Chris (Research fellow), editor, Taylor John B. editor, and Becker, Gary S. (Gary Stanley), 1930-2014, honouree, eds. Inequality and economic policy: Essays in honor of Gary Becker. Stanford, California: Hoover Institution Press, 2015.

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Book chapters on the topic "Beckner inequality"

1

Mavelli, Luca. "Sacred market, sacrificial lives (I)." In Neoliberal Citizenship, 142–72. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780192857583.003.0006.

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This and the next chapter discuss how the ascendancy of neoliberal biopolitics in the logics and practices of citizenship exceeds mere dynamics of economization, to encompass a fully-fledged process of sacralization of the market. Building on the thought of Giorgio Agamben, Chapter 6 explores a first trajectory of sacralization of the market: a process of totalizing commodification that, by leaving no domain or space beyond itself, turns the market into an overarching and unquestionable framework of meanings and significations. The implications of this sacralization are explored with reference to the neoliberal citizenship regimes advocated by economists Milton Friedman and Gary Becker. Whereas the former praises the illegalization of migration as beneficial for both the migrant and the host community, the latter supports the idea that citizenship should be for sale and the fact that those in need (nominal citizens and non-citizens alike) may sell their organs for cash. These accounts are oblivious to issues of inequality and exploitation. They reduce life and its biological components to commodities and subordinate citizenship to its capacity to contribute to the production of other commodities. Both accounts are shown to be a response to the problem of scarcity, which in turn will emerge as the other side of a problem of overabundance that sees neoliberal capitalism actively engaged in the biopolitical production and elimination of surplus populations.

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Conference papers on the topic "Beckner inequality"

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Lovett, Shachar, and Jiapeng Zhang. "Improved Noisy Population Recovery, and Reverse Bonami-Beckner Inequality for Sparse Functions." In STOC '15: Symposium on Theory of Computing. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2746539.2746540.

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