Abstract

Let q1(t,x), q2(t,x) belong to C(Rt;W1, infinity (Rx3)), qi(t,x)=0 for mod x mod > rho with some rho >0 and let KiHash be the corresponding generalized scattering kernels, i=1,2. The author proves that if q1>or=q2 and if K1Hash (s',- omega 0; s, omega 0)=K2Hash (s', - omega 0;s, omega 0) for some omega 0 in S2, then q1=q2. As a corollary, the author gets the following result. Let Vi(x) in Linfinity (R3), Vi has compact support and suppose that - Delta +Vi has no bound states, i=1, 2. Let ai be the scattering amplitude related to Vi, i=1, 2. Suppose that V1>or=V2 and for some omega 0 the author has a1(k,- omega 0, omega 0)=a2(k,- omega 0, omega 0) for all k. Then V1=V2.

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