On the inverse Sturm - Liouville problem on a finite interval.
In this paper the following boundary problem
is being considered: h and H are real
-y¢¢ + q(x)y = ly, x Î
(0,p), q Î Lp(0,p), (p = 1;2), (1) y¢(0) - hy(0) = 0, y¢(p) + Hy(p) = 0, (2)
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.
h and H are real