Relevant bibliographies by topics / Logarithmic Sobolev spaces

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Academic literature on the topic 'Logarithmic Sobolev spaces'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Logarithmic Sobolev spaces"

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Ghobber, Saifallah, and Hatem Mejjaoli. "Logarithm Sobolev and Shannon’s Inequalities Associated with the Deformed Fourier Transform and Applications." Symmetry 14, no. 7 (June 24, 2022): 1311. http://dx.doi.org/10.3390/sym14071311.

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By using the symmetry of the Dunkl Laplacian operator, we prove a sharp Shannon-type inequality and a logarithmic Sobolev inequality for the Dunkl transform. Combining these inequalities, we obtain a new, short proof for Heisenberg-type uncertainty principles in the Dunkl setting. Moreover, by combining Nash’s inequality, Carlson’s inequality and Sobolev’s embedding theorems for the Dunkl transform, we prove new uncertainty inequalities involving the L∞-norm. Finally, we obtain a logarithmic Sobolev inequality in Lp-spaces, from which we derive an Lp-Heisenberg-type uncertainty inequality and an Lp-Nash-type inequality for the Dunkl transform.
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Marton, Katalin. "Logarithmic Sobolev inequalities in discrete product spaces." Combinatorics, Probability and Computing 28, no. 06 (June 13, 2019): 919–35. http://dx.doi.org/10.1017/s0963548319000099.

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AbstractThe aim of this paper is to prove an inequality between relative entropy and the sum of average conditional relative entropies of the following form: for a fixed probability measure q on , ( is a finite set), and any probability measure on , (*) $$D(p||q){\rm{\le}}C \cdot \sum\limits_{i = 1}^n {{\rm{\mathbb{E}}}_p D(p_i ( \cdot |Y_1 ,{\rm{ }}...,{\rm{ }}Y_{i - 1} ,{\rm{ }}Y_{i + 1} ,...,{\rm{ }}Y_n )||q_i ( \cdot |Y_1 ,{\rm{ }}...,{\rm{ }}Y_{i - 1} ,{\rm{ }}Y_{i + 1} ,{\rm{ }}...,{\rm{ }}Y_n )),} $$ where pi(· |y1, …, yi−1, yi+1, …, yn) and qi(· |x1, …, xi−1, xi+1, …, xn) denote the local specifications for p resp. q, that is, the conditional distributions of the ith coordinate, given the other coordinates. The constant C depends on (the local specifications of) q.The inequality (*) ismeaningful in product spaces, in both the discrete and the continuous case, and can be used to prove a logarithmic Sobolev inequality for q, provided uniform logarithmic Sobolev inequalities are available for qi(· |x1, …, xi−1, xi+1, …, xn), for all fixed i and fixed (x1, …, xi−1, xi+1, …, xn). Inequality (*) directly implies that the Gibbs sampler associated with q is a contraction for relative entropy.In this paper we derive inequality (*), and thereby a logarithmic Sobolev inequality, in discrete product spaces, by proving inequalities for an appropriate Wasserstein-like distance.
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Chaabane, Slim, and Imed Feki. "Optimal logarithmic estimates in Hardy–Sobolev spaces." Comptes Rendus Mathematique 347, no. 17-18 (September 2009): 1001–6. http://dx.doi.org/10.1016/j.crma.2009.07.018.

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Edmunds, D. E., and H. Triebel. "Logarithmic Sobolev Spaces and Their Applications to Spectral Theory." Proceedings of the London Mathematical Society s3-71, no. 2 (September 1995): 333–71. http://dx.doi.org/10.1112/plms/s3-71.2.333.

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Hsu, Elton P. "Logarithmic Sobolev Inequalities on Path Spaces Over Riemannian Manifolds." Communications in Mathematical Physics 189, no. 1 (October 1, 1997): 9–16. http://dx.doi.org/10.1007/s002200050188.

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Gressman, Philip T. "Fractional Poincaré and logarithmic Sobolev inequalities for measure spaces." Journal of Functional Analysis 265, no. 6 (September 2013): 867–89. http://dx.doi.org/10.1016/j.jfa.2013.05.036.

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Ibrahim, H. "A Generalization of a Logarithmic Sobolev Inequality to the Hölder Class." Journal of Function Spaces and Applications 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/148706.

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In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality is originated from the Brézis-Gallouët-Wainger logarithmic type inequalities revealing Sobolev embeddings in the critical case. In this paper, we improve the parabolic version of Ogawa inequality by allowing it to cover not only the class of functions from Sobolev spaces, but also the wider class of Hölder continuous functions.
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Ehler, Martin, Manuel Gräf, and Chris J. Oates. "Optimal Monte Carlo integration on closed manifolds." Statistics and Computing 29, no. 6 (October 30, 2019): 1203–14. http://dx.doi.org/10.1007/s11222-019-09894-w.

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Abstract The worst case integration error in reproducing kernel Hilbert spaces of standard Monte Carlo methods with n random points decays as $$n^{-1/2}$$n-1/2. However, the re-weighting of random points, as exemplified in the Bayesian Monte Carlo method, can sometimes be used to improve the convergence order. This paper contributes general theoretical results for Sobolev spaces on closed Riemannian manifolds, where we verify that such re-weighting yields optimal approximation rates up to a logarithmic factor. We also provide numerical experiments matching the theoretical results for some Sobolev spaces on the sphere $${\mathbb {S}}^2$$S2 and on the Grassmannian manifold $${\mathcal {G}}_{2,4}$$G2,4. Our theoretical findings also cover function spaces on more general sets such as the unit ball, the cube, and the simplex.
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Aouaoui, Sami, and Rahma Jlel. "A new Singular Trudinger–Moser Type Inequality with Logarithmic Weights and Applications." Advanced Nonlinear Studies 20, no. 1 (February 1, 2020): 113–39. http://dx.doi.org/10.1515/ans-2019-2068.

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AbstractIn this paper, we establish a new singular Trudinger–Moser type inequality for radial Sobolev spaces with logarithmic weights. The existence of nontrivial solutions is proved for an elliptic equation defined in {\mathbb{R}^{n}}, relying on variational methods and involving a nonlinearity with doubly exponential growth at infinity.
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Machihara, Shuji, Tohru Ozawa, and Hidemitsu Wadade. "Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces." Journal of Inequalities and Applications 2013, no. 1 (2013): 381. http://dx.doi.org/10.1186/1029-242x-2013-381.

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Dissertations / Theses on the topic "Logarithmic Sobolev spaces"

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Park, Young Ja. "Sobolev trace inequality and logarithmic Sobolev trace inequality." Digital version:, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p9992883.

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Inahama, Yuzuru. "Logarithmic Sobolev Inequality on Free Loop Groups for Heat Ker-nel Measures Associated with the General Sobolev Spaces." 京都大学 (Kyoto University), 2001. http://hdl.handle.net/2433/150808.

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Ταβουλάρης, Νικόλαος Κ. "Ανισότητες Sobolev και εφαρμογές." 2004. http://nemertes.lis.upatras.gr/jspui/handle/10889/249.

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Η παρούσα διατριβή εντάσσεται ερευνητικά στην περιοχή της μη γραμμικής ανάλυσης και ειδικότερα στην εύρεση βέλτιστων σταθερών για ανισότητες Sobolev στο χώρο Rn με ανώτερης τάξης δεκαδικές παραγώγους. Επίσης, δίνονται οι αντίστοιχες βέλτιστες σταθερές αυτών των ανισοτήτων πάνω στη σφαίρα Sn με τη χρησιμοποίηση ως βασικού εργαλείου την στερεογραφική προβολή. Τέλος, σαν μια εφαρμογή των ευρεθέντων ανισοτήτων έχουμε ένα θεώρημα σχετικό με αυτό των Rellich-Kondrashov και το οποίο είναι εξαιρετικής σημασίας, ιδιαίτερα στο λογισμό των μεταβολών.
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Book chapters on the topic "Logarithmic Sobolev spaces"

1

Üstünel, A. S. "Damped Logarithmic Sobolev Inequality on the Wiener Space." In Stochastic Analysis and Related Topics VII, 245–49. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0157-1_11.

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Eldan, Ronen, and Michel Ledoux. "A Dimension-Free Reverse Logarithmic Sobolev Inequality for Low-Complexity Functions in Gaussian Space." In Lecture Notes in Mathematics, 263–71. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36020-7_12.

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Journal articles
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