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.

chapter Chapter 1|38 pages

Matrix-Valued Functions

chapter Chapter 2|48 pages

Functions of Compact Operators

chapter Chapter 3|37 pages

Functions of Nonselfadjoint Operators

chapter Chapter 5|9 pages

Perturbations of Noncompact Operators

chapter Chapter 8|26 pages

Stability of Retarded Systems

chapter Chapter 10|23 pages

Stability of Semilinear Parabolic Systems

chapter Chapter 12|18 pages

Semilinear Boundary Value Problems