By Ishiguro M., Sakamoto Y.

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1 for scientific schools. Appendix A. t Ut = 1- i I’ dt’(Dbi, + Dtbr)Uti . Gt = 1+ i 1 dt’(Dbi, + Dtbtl)ctj satisfies t Consider the iterated series U ( N )for the solution of the integral equation with the initial condition u(0)= and relation 1 41 and the same series for 6 with the initial condition 6p)= 1. The limit of the series (which exists under our assumptions) is the solution of the integral equation We want to prove that for t 2 T h btUT = UTbt - ~ ~ - D X [ O , T ] ( ~ ) U T . 1) Let us prove the following relation for the iterated series (for t btU$N)= @"bt -iy-D~[o,~](t)U$~-~).

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