Solution of the inverse problem on the half-line

In view of (1.35) this leads us to conclude that for each fixed x the matrix-valued function V(x,X) is an entire analytic function in Λ. Using (137) and Liouville’s theorem ([94, p. 209]), we get that 'Ριι(χ,Α) = 1, V \ jb(æ,Λ) = 0 for k = 2, n. But then Фш(а;,А) = Фт (х,А) for all x, A and m, and hence L — L. Theorem 1.2 is proved.