Boundary values of solutions of operator-differential equations of an arbitrary order (Q914034)

The theory of boundary values of solutions to the operator-differential equations of the form \[ (1)\quad y^{(n)}(t)+\sum^{n}_{k=1}P_ n(A)y^{(n-k)}(t)=0 \] is studied, where \(P_ k(A)=\sum^{p_ k}_{i=1}a_{k_ i}A^ i\) are polynomials of order \(p_ k\) of a selfadjoint operator A in a separable Hilbert space H. Under some conditions the boundary values of solutions of (1) are shown to belong to certain spaces of ordinary functions or distributions.