Initial data of solutions of complete second-order operator-differential equations (Q1971745)

The very well organized paper describes the space of all initial conditions for the Cauchy problem \[ y''(t)+ A(t) y'(t)+ B(t) y(t)= 0,\quad y(0)= f_1,\quad y'(0)= f_2,\tag{1} \] which ensure a unique, global solution. (1) represents a second-order operator-differential equation. \(A\), \(B\) represent commuting, normal operators on a complex separable Hilbert space. For \(A= 0\) and \(B\) nonnegative and selfadjoint a characterization of the above problem was done by Goldstein and Gorbachuk, for the wave equation by S. L. Sobolev. The paper contains similar results for (1).