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Inverse scattering. III. Three dimensions, continued
1.R. G. Newton, J. Math. Phys. 21, 1698 (1980). This paper will be referred to as II.
2.Another solution has been given by L. D. Faddeev, Itogi Nauk. Tekh. Sov. Probl. Mat. 3, 93 (1974)
2.[L. D. Faddeev, J. Sov. Math. 5, 334 (1976)].
3.We remind the reader that x is a point in is a point on (or a unit vector in ); is the scattering amplitude, which we regard as the kernel of an operator family on We use † for the Hermitian adjoint and * for the complex conjugate.
4. denotes the Hilbert‐Schmidt norm, where tr denotes the traceon
5.These are (3.4) and (3.6) of II.
6.It also follows that if then this leads to Lemma 6.1 of II.
7.If is the operator on of multiplication by and is the projection on then is a projection on but it is not self‐adjoint.
8.D. Ludwig, Commun. Pure Appl. Math. 19, 49 (1966), Theorem 4.9, p. 60.
9. is the upper half of the complex plane.
10.See, for example, R. G. Newton, Scatlering Theory of Wavea and Particles (McGraw‐Hili, New York, 1966), p. 348.
11.The tilde denotes the operator whose kernel is the transpose.
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