Results 11 to 20 of about 435 (135)
Sharp exponential inequalities for the Ornstein-Uhlenbeck operator [PDF]
Journal of Functional Analysis, 2021 The optimal constants in a class of exponential type inequalities for the Ornstein-Uhlenbeck operator in the Gauss space are detected. The existence of extremal functions in the relevant inequalities is also established. Our results disclose analogies and dissimilarities in comparison with Adams' inequality for the Laplace operator, a companion of our ...
Cianchi A., Musil V., Pick L.
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Some remarks on degenerate hypoelliptic Ornstein–Uhlenbeck operators
Journal of Mathematical Analysis and Applications, 2015 We study degenerate hypoelliptic Ornstein-Uhlenbeck operators in $L^2$ spaces with respect to invariant measures. The purpose of this article is to show how recent results on general quadratic operators apply to the study of degenerate hypoelliptic Ornstein-Uhlenbeck operators.
Ottobre, Michela +2 more
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BLO spaces associated with the Ornstein–Uhlenbeck operator
Bulletin des Sciences Mathématiques, 2008 Let \((\mathbb{R}^n, | \cdot |, d\gamma )\) be the Gauss measure metric space, where \(\mathbb{R}^n\) denotes the \(n\)-dimensional Euclidean space, \(| \cdot |\) the Euclidean norm and \(d\gamma = \pi^{-n/2}e^{- | x |^2}dx\) the Gauss measure. \textit{G. Mauceri} and \textit{S. Meda} [J. Funct. Anal. 252, 278--313 (2007; Zbl 1136.46027)] defined \(BMO(
Liu, Liguang, Yang, Dachun
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On the eigenfunctions of the complex Ornstein–Uhlenbeck operators [PDF]
Kyoto Journal of Mathematics, 2014 16pages
Chen, Yong, Liu, Yong
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Bruno Pini Mathematical Analysis SeminarLet $\mathcal{L}$ be the hypoelliptic Ornstein-Uhlenbeck operator associated with the pair of matrices (A,B). In 2004, Priola and Zabczyk proved the following Liouville-type theorem: every bounded entire solution of $\mathcal{L}u=0$ is constant if and ...
Alessia E. Kogoj +2 more
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Hypercontractivity, Hopf-Lax type formulas, Ornstein-Uhlenbeck operators (II)
Discrete & Continuous Dynamical Systems - S, 2009 In this paper we study Hopf-Lax formulas, hypercontractivity, ultracontractivity, logarithmic Sobolev inequalities for a class of first order Hamilton-Jacobi equations.
AVANTAGGIATI A, LORETI, Paola
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On basin of zero-solutions to a semilinear parabolic equation with Ornstein-Uhlenbeck operator
Journal of Inequalities and Applications, 2006 We consider the basin of the zero-solution to a semilinear parabolic equation on with the Ornstein-Uhlenbeck operator. Our aim is to show that the Ornstein-Uhlenbeck operator contributes to enlargement of the basin by using the logarithmic Sobolev ...
Fujita Yasuhiro
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On the Cauchy problem for non-local Ornstein–Uhlenbeck operators [PDF]
Nonlinear Analysis, 2016 We study the Cauchy problem involving non-local Ornstein-Uhlenbeck operators in finite and infinite dimensions. We prove classical solvability without requiring that the Lévy measure corresponding to the large jumps part has a first finite moment. Moreover, we determine a core of regular functions which is invariant for the associated transition Markov
PRIOLA, Enrico, Stefano Traca'
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Some remarks on infinite-dimensional nonlinear elliptic problems
Electronic Journal of Differential Equations, 2007 We discuss some nonlinear problems associated with an infinite dimensional operator $L$ defined on a real separable Hilbert space $H$. As the operator $L$ we choose the Ornstein-Uhlenbeck operator induced by a centered Gaussian measure $mu$ with ...
Philippe Clement +2 more
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Holomorphy of spectral multipliers of the Ornstein–Uhlenbeck operator
Journal of Functional Analysis, 2004 The closure \(\mathcal L\) of the Ornstein--Uhlenbeck operator has spectral resolution \[ {\mathcal L}f=\sum_{n=0}^\infty n P_n f, \] where \(P_n\) is the orthogonal projection onto the linear span of Hermite polynomials of degree \(n\) in \(d\) variables.
HEBISCH W., MAUCERI, GIANCARLO, MEDA S.
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