Translations of Mathematical Monographs 1970; 430 pp; softcover Volume: 24 ISBN10: 0821836277 ISBN13: 9780821836279 List Price: US$129 Member Price: US$103.20 Order Code: MMONO/24.S
 An abstract Volterra operator is, roughly speaking, a compact operator in a Hilbert space whose spectrum consists of a single point \(\lambda=0\). The theory of abstract Volterra operators, significantly developed by the authors of the book and their collaborators, represents an important part of the general theory of nonselfadjoint operators in Hilbert spaces. The book, intended for all mathematicians interested in functional analysis and its applications, discusses the main ideas and results of the theory of abstract Volterra operators. Of particular interest to analysts and specialists in differential equations are the results about analytic models of abstract Volterra operators and applications to boundary value problems for ordinary differential equations. Readership Graduate students and research mathematicians interested in functional analysis and its applications. Table of Contents  Introduction
 Abstract triangular representation of completely continuous operators
 General theorems on transformators
 The transformator of triangular truncation. Relations between the spectra of the hermitian components of Volterra operators
 The factorization of operators which are close to the unit operator
 Triangular models of Volterra operators
 Selfadjoint boundary value problems for a canonical equation. Tests for the stable boundedness of the solutions of a canonical equation with a periodic \(H\)matrix
 Fundamental theorem on the density of the spectrum of the real component of a Volterra operator with nuclear imaginary component
 Appendix. Unicellular operators and related analytic problems
 Bibliography
 Index
