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

Authors:	A H Khater M S Saif K El Rashidy

Institution:	(1) Mathematics Department, Faculty of Science, Beni-seuf University, Beni-seuf, Egypt;(2) Mathematics Department, Faculty of Science, Fayoum University, Fayoum, Egypt

Abstract:	The aim of the present paper is to study the existence and the completeness of the wave operators $\cal{W}_{\pm}(H,H_{0})$ for elliptic operators of higher order (Schr?dinger operator) with short-range potential of the form: $H = \sum_{\|\alpha\|,\|\beta\| \leq m}(-1)^{\|\alpha\|} D^{\alpha}(b_{\alpha \beta}(x)D^{\beta})+V_{0}+V$ and other related results by using the trace class method. MSC: 2000 46N50, 47Dxx, 47F05.

Keywords:	wave operator trace class method partial differential operator
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