Fast decaying potentials on the finite-gap background and the ∂-bar-problem on the Riemann surfacesстатья
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Дата последнего поиска статьи во внешних источниках: 13 января 2015 г.
Аннотация:The direct and the inverse ‘scattering problems’ for the heat-conductivity operator TeX are studied for the following class of potentials:u(x,y)=u_0 (x,y)+u_1(x,y), where u_0(x,y) is a nonsingular real finite-gap potential and u_1(x,y) decays sufficiently fast as x^2+y^2→∞. We show that the ‘scattering data’ for such potentials is the TeX data on the Riemann surface corresponding to the potential u_0 (x,y). The ‘scattering data’ corresponding to real potentials is characterized and it is proved that the inverse problem corresponding to such data has a unique nonsingular solution without the ‘small norm’ assumption. Analogs of these results for the fixed negative energy scattering problem for the two-dimensional time-independent Schrödinger operator are obtained.