V. A. Yavrian

On the inverse Sturm - Liouville problem on a finite interval.

   In this paper the following boundary problem is being considered:
-y + q(x)y = ly,   x (0,p),    q Lp(0,p),   (p = 1;2),
(1)
y(0) - hy(0) = 0,    y(p) + Hy(p) = 0,
(2)

h and H are real numbers.
   The following question is solved: Under which conditions the sequences l0 < l1 < l2 < ... and 0 < r0 < r1 < ... are the eigenvalues and the normalizing numbers for some boundary problem (1), (2). Tne answer is given in terms of an asymptotical behaviour of these sequences.
   It is also studied the problem of unique restoration of the boundary problem (1) , (2) by spectrum only and numbers h and H.