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Theory and Applications of Volterra Operators in Hilbert Space
I. C. Gohberg and M. G. Krein

Translations of Mathematical Monographs
1970; 430 pp; softcover
Volume: 24
ISBN-10: 0-8218-3627-7
ISBN-13: 978-0-8218-3627-9
List Price: US$129
Member Price: US$103.20
Order Code: MMONO/24.S
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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 non-self-adjoint 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.


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
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