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Rapidly decreasing potentials on a background of finite-zone potentials and the $$\bar\partial$$-problem on Riemann surfaces. (English. Russian original) Zbl 0748.35025
Funct. Anal. Appl. 23, No. 4, 321-322 (1989); translation from Funkts. Anal. Prilozh. 23, No. 4, 79-80 (1989).
The scattering theory for the operators $$L_ p=\partial_ y-\partial^ 2_ x+u(x,y)$$, $$L_ s=-\partial^ 2_ x-\partial^ 2_ y+u(x,y)$$ is studied. The energy $${\mathcal E}_ 0$$ is fixed and the potential $$u(x,y)$$ has the form $$u(x,y)=u_ 0(x,y)+u_ 1(x,y)$$, where $$u_ 0(x,y)$$ is a finite-zone potential, $$u_ 1 (x,y)$$ is a quickly decreasing potential.

##### MSC:
 35P25 Scattering theory for PDEs 35N15 $$\overline\partial$$-Neumann problems and formal complexes in context of PDEs
##### Keywords:
finite-zone potential; quickly decreasing potential
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##### References:
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