Intended for specialists in functional analysis and stability theory, this work presents a systematic exposition of estimations for norms of operator-valued functions, and applies the estimates to spectrum perturbations of linear operators and stability theory. The author demonstrates his own approach to spectrum perturbations.
". . .provides valuable new working tools and is well worth reading for anyone seriously interested in the area of the theory of matrices or operator theory. "
---Applications of Mathematics
". . .well written and useful. . .presents a systematic exposition of. . .a subject to which the author has made substantial contributions. "
Matrix-valued functions; functions of compact operators; functions of nonself-adjoint operators; perterbations of finite dimensional and compact operators; perterbations of noncompact operators; perterbations of operators on a tensor product of Hilbert spaces; stability and boundedness of ordinary differential systems; stability of retarded systems; absolute stability of solutions of Voletta integral equations; stability of semilinear parabolic systems; stability of Volterra integrodifferential systems and applications to viscoelasticity; semilinear boundary value problems; list of main symbols.