Translation of [Razlozhenie po sobstvennym funkt︠s︡ii︠a︡m samosopri︠a︡zhennykh operatorov]
Includes bibliographical references (pages 769-799).
Introduction -- Spaces with negative norms and generalized functions -- Boundary value problems. General concepts -- Boundary value problems and smooth generalized solutions for elliptic equations. Green's function -- Boundary value problems. Other types of equations -- General theory of expansions of selfadjoint operators in generalized eigenvectors -- Spectral theory for selfadjoint partial differential operators -- Spectral theory of selfadjoint difference operators -- Representation of a positive definite kernel in terms of elementary kernels