TY - JOUR
AU - Metoui, Imen
AB - It is shown that the Ornstein–Uhlenbeck operator perturbed by a multipolar inverse square potential AΦ,G+V=Δ-∇Φ·∇+G·∇+∑i=1nc|x-ai|2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\begin{aligned} A_{\Phi ,G}+V=\Delta -\nabla \Phi \cdot \nabla +G\cdot \nabla +\sum \limits _{i=1}^{n}\frac{c}{|x-a_{i}|^{2}} \end{aligned}$$\end{document}with suitable domain generates a quasi-contractive and positive analytic C0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$C_{0}$$\end{document}-semigroup on the weighted space L2(RN,dμ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^{2}(\mathbb {R}^{N},d\mu )$$\end{document}, where dμ=exp(-Φ(x))dx\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$d\mu =\exp (-\Phi (x))dx$$\end{document}, Φ∈C2(RN,R)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Phi \in C^{2}(\mathbb {R}^{N}, \mathbb {R})$$\end{document}, G∈C1(RN,RN)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$G \in C^{1}(\mathbb {R}^{N},\mathbb {R}^{N})$$\end{document}, c>0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$c>0$$\end{document}, and a1,…,an∈RN\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$a_{1},\ldots , a_{n}\in \mathbb {R}^{N}$$\end{document}. The proofs are based on an L2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^{2}$$\end{document}-weighted Hardy inequality and bilinear form techniques.
TI - Generalized Ornstein–Uhlenbeck operators perturbed by multipolar inverse square potentials in L2\documentclass[12pt]{minimal} \usepackage{amsmath} ...
JF - Archiv der Mathematik
DO - 10.1007/s00013-021-01625-w
DA - 2021-10-01
UR - https://www.deepdyve.com/lp/springer-journals/generalized-ornstein-uhlenbeck-operators-perturbed-by-multipolar-wbH0AsL8ON
SP - 433
EP - 440
VL - 117
IS - 4
DP - DeepDyve
ER -