Theory and Applications of Volterra Operators in Hilbert Space

• ISBN13: 9780821836279
• ISBN10: 0821836277
• Format: Paperback
• Copyright: 2004-06-16
• Publisher: Amer Mathematical Society

Summary

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.

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

Table of Contents provided by Publisher. All Rights Reserved.