{"title":"On the $L^p$ boundedness of the wave operators for fourth order Schrödinger operators","authors":"M. Goldberg, William R. Green","doi":"10.1090/tran/8377","DOIUrl":null,"url":null,"abstract":"We consider the fourth order Schr\\\"odinger operator $H=\\Delta^2+V(x)$ in three dimensions with real-valued potential $V$. Let $H_0=\\Delta^2$, if $V$ decays sufficiently and there are no eigenvalues or resonances in the absolutely continuous spectrum of $H$ then the wave operators $W_{\\pm}= s\\,-\\,\\lim_{t\\to \\pm \\infty} e^{itH}e^{-itH_0}$ extend to bounded operators on $L^p(\\mathbb R^3)$ for all $1","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tran/8377","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
We consider the fourth order Schr\"odinger operator $H=\Delta^2+V(x)$ in three dimensions with real-valued potential $V$. Let $H_0=\Delta^2$, if $V$ decays sufficiently and there are no eigenvalues or resonances in the absolutely continuous spectrum of $H$ then the wave operators $W_{\pm}= s\,-\,\lim_{t\to \pm \infty} e^{itH}e^{-itH_0}$ extend to bounded operators on $L^p(\mathbb R^3)$ for all $1