  An elliptic equation of order $2m$ with general nonlocal boundary-value
conditions, in a plane bounded domain $G$ with piecewise smooth boundary, is
considered. Generalized solutions belonging to the Sobolev space $W_2^m(G)$ are
studied. The Fredholm property of the unbounded operator corresponding to the
elliptic equation, acting on $L_2(G)$, and defined for functions from the space
$W_2^m(G)$ that satisfy homogeneous nonlocal conditions is proved.
