Results 101 to 110 of about 435 (135)

The Ornstein–Uhlenbeck Operator and the Ornstein–Uhlenbeck Semigroup

2019
In this chapter we are going to define and study the Ornstein–Uhlenbeck operator and the Ornstein–Uhlenbeck semigroup. They are analogous, in the Gaussian harmonic analysis, to the Laplacian and the heat semigroup in the classical case. Then, we study an important property of the Ornstein–Uhlenbeck semigroup, the hypercontractivity property, and some ...
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Sharp estimates for the Ornstein-Uhlenbeck operator

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2009
The purpose of this paper is to obtain a sharp functional calculus for the Ornstein-Uhlenbeck operator \(T\) acting on the \(L^p\) spaces with respect to the Gaussian measure \(\gamma\) on \(\mathbb R^d\). The authors prove a sharp estimate of the operator norm of the imaginary powers of \(T\) on \(L^p(\gamma), \quad ...
MAUCERI, GIANCARLO, MEDA S., SJOGREN P.
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Heat kernels for generalized Ornstein–Uhlenbeck operators

Applicable Analysis, 2014
In this article, we use the Hamiltonian and Lagrangian formalism to study the -dimensional extended Ornstein–Uhlenbeck operator where is an real matrix, is a real parameter and means the gradient. Given the boundary conditions, we find the solutions of the associated Hamiltonian system of .
Der-Chen Chang, Nanping Yang
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An identification problem for the Ornstein–Uhlenbeck operator

jiip, 2011
Abstract We consider the problem of identifying the constant α ∈ ℝ in the Cauchy problem , when , from an additional measurement on the solution u.
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Geometric Analysis on Ornstein–Uhlenbeck Operators with Quadratic Potentials

The Journal of Geometric Analysis, 2012
The paper focuses on Ornstein-Uhlenbeck operators perturbed by quadratic potentials. Through Hamiltonian formalism, induced geodesics are explicitly determined and heat kernels are constructed.
Chang, Der-Chen, Feng, Sheng-Ya
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On a Dirichlet Problem Involving an Ornstein–Uhlenbeck Operator

Potential Analysis, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Functional calculus for some perturbations of the Ornstein–Uhlenbeck operator

Mathematische Zeitschrift, 2008
\textit{J.\,García--Cuerva, G.\,Mauceri, S.\,Meda, P.\,Sjögren} and \textit{J.\,L.\thinspace Torrea} [J.~Funct.\ Anal.\ 183, No.\,2, 413--450 (2001; Zbl 0995.47010)] proved that for every \(p>1\), the Ornstein--Uhlenbeck operator has a bounded holomorphic functional calculus in \(L^p\)-spaces.
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\(L^p\)-spectrum of Ornstein-Uhlenbeck operators

2001
In this paper the author considers the spectrum of drift operators \(\mathcal L = \sum_{i,j=1}^n b_{ij}x_j D_i\) and the Ornstein--Uhlenbeck operators \({\mathcal A}= \sum_{i,j=1}^n q_{ij} D_{ij}+ \mathcal L\) in \(L^p(\mathbb R^n)\) and \(BUC(\mathbb R^n)\).
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Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Science Advances, 2021
Sifan Wang, Hanwen Wang
exaly  

Global estimates for degenerate Ornstein-Uhlenbeck operators

2010
We consider a class of degenerate hypoelliptic Ornstein–Uhlenbeck operators in RN. For this class of operators we prove global L p estimates (1 < p < ∞) and corresponding weak type (1,1) estimates. This result seems to be the first case of global estimates, in Lebesgue L p spaces, for complete Hörmander’s operators.
BRAMANTI, MARCO, G. CUPINI, E. LANCONELLI, E. PRIOLA   +3 more
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