Resolvent approach for the nonstationary Schrodinger equation

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Abstract
The spectral transform for the nonstationary Schrodinger equation is considered. The resolvent operator of the Schrodinger equation is introduced and the Fourier transform of its kernel (called the resolvent function) is studied. It is shown that it can be used to construct a generalized version of the theory of the spectral transform which enables one to handle also potentials approaching zero in every direction except a finite number, which corresponds to the physical situation of long waves mutually interacting in the plane.