More precisely, we shall show the existence of the Miller wave operators.We restrict ourselves to solutions with finite energy. For pa rs f={fi 9 fz} of functions in R n the energy is defined by f JE where Df 1 =(D 1 f l9 -" 9 D n f 1 ) (D, = d/dx,) and 12/11'= S A/11 8 . The
.7=1Hilbert space M is defined as the completion in the energy norm of Communicated by S. Matsuura,
Let £1 c: R^ be an unbounded domain with smooth boundary 9O. We consider the mixed initial-boundary value problem For solution w (t} of(l.l), we simply write and call it the energy of w (t) at time t.
In this paper inverse problems for the Sturm-Liouville operator are studied. A set of values of the logarithmic derivative of eigenfunctions at some internal point and parts of two spectra are taken as data. Uniqueness theorems are obtained. The approach that was used in investigation of problems with partially known potential is employed.
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