ENSS' Theory in Long Range Scattering: Second Order Hyperbolic and Parabolic Operators

✍ Scribed by Pl. Muthuramalingam

• Publisher: John Wiley and Sons
• Year: 1986
• Tongue: English
• Weight: 748 KB
• Volume: 127
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19861270110

✦ Synopsis

We prove asymptotic completeness using ENSS' method for ho(P) + W,(Q) + W,(Q) whereho: Rn+R is a polynomial of degree 2 with lim (ho(5)I +lvh,(l)l=-, Wa a short range potential and RIL a smooth long range potential. K'--Q 1. Introduction In [lo] we showed the possibility of developing the "geometric method" of ENSS [3], for hyperbolic operators in L2(RZ) with short range potentials. For ENSS' method see [11, 141 and references therein. Using [2] we refined [lo] to [ 121 to include a class of simply characteristic operators withshort rangepotentials. For this class a stationary theory was already established in [4]. In [13] we established the existence of the wave operators for h,(P) + W , + W,(Q, P) where h,, can include the parabolic operators h&,, t2) =t:k t2, on Rz as well. The result of [5] while including the hyperbolic operator 6: -ti on Rz, i t excludes the parabolic operator [:* t2 on Rz. In this article we extend [ 121 to simply characteristic operators of order 2 with long range potentials.