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Algorithmically Verifiable Characterization of the Class of Scattering Amplitudes for Small



Abstract. A necessary and sufficient condition for a function A(0’,6’,k)P, 0 E S’, k E R+ = (0, oa) to be the scattering amplitude corresponding to a local potential q(zl E Qp:= {P I P = 5 IPI 5 41 + blP}, 0> 3, is given under the assumption that 11 A II< 2*k- ’ for all k> 0, where 1) A II is the norm of A: L2(S2)- L2(S2). The condition is algorithmically verifiable. I. Introduction. The first characterization of the class A of scattering amplitudes corresponding to local potentials q E Qp: = {q 1 q = ~9 14 5 ccl+ 14>+‘, P> 3) was given in [l]. This characterization can be described as follows. Consider the equatio

Year: 2012
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