scholarly journals Sur l'existence de l'operateur carré du champ

1986 ◽  
pp. 30-33
Author(s):  
P. A. Meyer
Keyword(s):  
Carré Du Champ

scholarly journals Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications

2021 ◽  
Author(s):  
Lorenzo Dello Schiavo
Keyword(s):  
Radon Measure ◽  
Measure Space ◽  
Probability Space ◽  
Dirichlet Space ◽  
Dirichlet Forms ◽  
Dirichlet Spaces ◽  
Ergodic Decomposition ◽  
Direct Integral ◽  
Unique Representation ◽  
Carré Du Champ

AbstractWe study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique.

scholarly journals L'opérateur carré du champ: un contre-exemple

1989 ◽  
pp. 324-325
Author(s):  
G. Mokobodzki
Keyword(s):  
Carré Du Champ

L'operateur carré du champ

1976 ◽  
pp. 142-161 ◽  
Author(s):  
P. A. Meyer
Keyword(s):  
Carré Du Champ

scholarly journals Interpolation inequalities in \begin{document}$ \mathrm W^{1,p}( {\mathbb S}^1) $\end{document} and carré du champ methods

2020 ◽  
Vol 40 (1) ◽  
pp. 375-394
Author(s):  
Jean Dolbeault ◽  
◽  
Marta García-Huidobro ◽  
Rául Manásevich ◽  
◽  
...  
Keyword(s):  
Interpolation Inequalities ◽  
Carré Du Champ

scholarly journals Quantitative Fourth Moment Theorem of Functions on the Markov Triple and Orthogonal Polynomials

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yoon Tae Kim ◽  
Hyun Suk Park
Keyword(s):  
Probability Measure ◽  
Orthogonal Polynomials ◽  
Normal Approximation ◽  
Random Variables ◽  
Random Variable ◽  
New Technique ◽  
Fourth Moment ◽  
Markov Diffusion ◽  
Carré Du Champ ◽  
A New Technique

In this paper, we consider a quantitative fourth moment theorem for functions (random variables) defined on the Markov triple E , μ , Γ , where μ is a probability measure and Γ is the carré du champ operator. A new technique is developed to derive the fourth moment bound in a normal approximation on the random variable of a general Markov diffusion generator, not necessarily belonging to a fixed eigenspace, while previous works deal with only random variables to belong to a fixed eigenspace. As this technique will be applied to the works studied by Bourguin et al. (2019), we obtain the new result in the case where the chaos grade of an eigenfunction of Markov diffusion generator is greater than two. Also, we introduce the chaos grade of a new notion, called the lower chaos grade, to find a better estimate than the previous one.

scholarly journals Improved Interpolation Inequalities and Stability

2020 ◽  
Vol 20 (2) ◽  
pp. 277-291
Author(s):  
Jean Dolbeault ◽  
Maria J. Esteban
Keyword(s):  
Euclidean Space ◽  
Symmetry Breaking ◽  
Stereographic Projection ◽  
Optimal Interpolation ◽  
Stability Estimates ◽  
Interpolation Inequalities ◽  
Carré Du Champ ◽  
Optimal Constants ◽  
Optimal Functions

AbstractFor exponents in the subcritical range, we revisit some optimal interpolation inequalities on the sphere with carré du champ methods and use the remainder terms to produce improved inequalities. The method provides us with lower estimates of the optimal constants in the symmetry breaking range and stability estimates for the optimal functions. Some of these results can be reformulated in the Euclidean space using the stereographic projection.

DIFFUSION PROCESSES ON PATH SPACES WITH INTERACTIONS

2001 ◽  
Vol 13 (02) ◽  
pp. 199-220 ◽  
Author(s):  
YUU HARIYA ◽  
HIROFUMI OSADA
Keyword(s):  
Diffusion Processes ◽  
Gibbs Measures ◽  
Infinite Volume ◽  
Gaussian Measures ◽  
Uhlenbeck Process ◽  
Mild Conditions ◽  
Carré Du Champ ◽  
Form Theory ◽  
The One ◽  
Non Gaussian

We construct dynamics on path spaces C (ℝ; ℝ) and C([-r, r];ℝ) whose equilibrium states are Gibbs measures with free potential φ and interaction potential ψ. We do this by using the Dirichlet form theory under very mild conditions on the regularity of potentials. We take the carré du champ similar to the one of the Ornstein–Uhlenbeck process on C([0, ∞);ℝ). Our dynamics are non-Gaussian because we take Gibbs measures as reference measures. Typical examples of free potentials are double-well potentials and interaction potentials are convex functions. In this case the associated infinite-volume Gibbs measures are singular to any Gaussian measures on C(ℝ;ℝ).

scholarly journals Sobolev Algebras Through a ‘Carré Du Champ’ Identity

2018 ◽  
Vol 61 (4) ◽  
pp. 1041-1054
Author(s):  
Frédéric Bernicot ◽  
Dorothee Frey
Keyword(s):  
Sobolev Spaces ◽  
Carré Du Champ

AbstractWe consider abstract Sobolev spaces of Bessel-type associated with an operator. In this work, we pursue the study of algebra properties of such functional spaces through the corresponding semigroup. As a follow-up to our previous work, we show that by making use of the property of a ‘carré du champ’ identity, this algebra property holds in a wider range than previously shown.

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