{"title":"Maximal estimates for the Fokker–Planck operator with magnetic field","authors":"Zeinab Karaki","doi":"10.4171/JST/369","DOIUrl":null,"url":null,"abstract":"We consider the Fokker-Planck operator with a strong external magnetic field. We show a maximal type estimate on this operator using a nilpotent approach on vector field polynomial operators and including the notion of representation of a Lie algebra. This estimate makes it possible to give an optimal characterization of the domain of the closure of the considered operator.","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2019-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Spectral Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/JST/369","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We consider the Fokker-Planck operator with a strong external magnetic field. We show a maximal type estimate on this operator using a nilpotent approach on vector field polynomial operators and including the notion of representation of a Lie algebra. This estimate makes it possible to give an optimal characterization of the domain of the closure of the considered operator.
期刊介绍：
The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome.
The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory.
Schrödinger operators, scattering theory and resonances;
eigenvalues: perturbation theory, asymptotics and inequalities;
quantum graphs, graph Laplacians;
pseudo-differential operators and semi-classical analysis;
random matrix theory;
the Anderson model and other random media;
non-self-adjoint matrices and operators, including Toeplitz operators;
spectral geometry, including manifolds and automorphic forms;
linear and nonlinear differential operators, especially those arising in geometry and physics;
orthogonal polynomials;
inverse problems.
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