This survey gives an account of the state of the art of the theory of Ornstein–Uhlenbeck
operators and semigroups. The domains of definition and the spectra of such operators are …

The method of semigroups is a unifying, widely applicable, general technique to formulate
and analyze fundamental aspects of fractional powers of operators L and their regularity …

Classical harmonic analysis dates back to the beginning of the nineteenth century and has
its roots in the study of Fourier series, the Fourier transform, and the development of tools …

Этот обзор посвящен современному состоянию теории операторов и полугрупп
Орнштейна–Уленбека, в том числе сравнительно недавним достижениям и открытым …

Let $ L $ be either the Hermite or the Ornstein-Uhlenbeck operator on $\mathbb {R}^ d $. We
find optimal integrability conditions on a function $ f $ for the existence of its heat and …

Consider the Schrödinger operator L=-Δ+ VL=-Δ+ V in R^ n, n ≥ 3, R n, n≥ 3, where V is a
nonnegative potential satisfying a reverse Hölder condition of the type (1| B| ∫ _B V (y) …

We introduce a pointwise definition of Lipschitz (also called Hölder) spaces adapted to the
parabolic Hermite operator H= ∂ _t-Δ _x+| x|^ 2 H=∂ t-Δ x+| x| 2 on R^ n+ 1 R n+ 1. Also for …

In this paper, we characterize the discrete Hölder spaces by means of the heat and Poisson
semigroups associated with the discrete Laplacian. These characterizations allow us to get …

Abstract Let H=− Δ+∣ x∣ 2 be a Hermite operator, where Δ is the Laplacian on ℝ n. In this
paper, we give a new characterization of the Besov space associated with Hermite operator …

We prove that for solutions of the Ornstein–Uhlenbeck or Hermite equations on the upper
half-space, in the Poisson setting, the nontangential limits and nontangetial boundedness …