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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 4, Pages 791-794

The Cauchy problem of the one dimensional Schrödinger equation with non-local potentials

Department of Mathematics, University of Patras, Patras, Greece

Received 16 July 1992

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For a large class of operators A, not necessarily local, it is proved that the Cauchy problem of the Schrödinger equation: d2f(z)dz2+Af(z)=s2f(z), f(0)=0, f(0)=1 possesses a unique solution in the Hilbert (H2(Δ)) and Banach (H1(Δ)) spaces of analytic functions in the unit disc Δ={z:|z|<1}.