Existence and Completeness of the Wave Operators for Higher Order Differential Operators

The aim of the present paper is to study the existence and the completeness of the wave operators \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cal{W}_{\pm}(H,H_{0})$$\end{document} for elliptic operators of higher order (Schrödinger operator) with short-range potential of the form: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ H = \sum_{|\alpha|,|\beta| \leq m}(-1)^{|\alpha|} D^{\alpha}(b_{\alpha \beta}(x)D^{\beta})+V_{0}+V$$\end{document} and other related results by using the trace class method.