Inequalities for the transformation operators and applications

Details Inequalities for the transformation operators and applications Inequalities for the transformation operators and applications

2003-01-31

arxiv.org/abs/math/0301383v1

Mathematics

Classical Analysis and ODEs

Scientific paper

Inequalities for the transformation operator kernel $A(x,y)$ in terms of $F$-function are given, and vice versa. These inequalities are applied to inverse scattering on half-line. Characterization of the scattering data corresponding to the usual scattering class $L_{1,1}$ of the potentials, to the class of compactly supported potentials, and to the class of square integrable potentials is given. Invertibility of each of the steps in the inversion procedure is proved.

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