Singular Bilinear Integrals

The integration of vector valued functions with respect to vector valued measures, especially spectral measures, is developed in view of applications in operator theory, scattering theory and semiclassical approximation in quantum physics. New techniques are developed for bilinear integration in cases where the classical approach does not apply.

Contents:

• Introduction
• Decoupled Bilinear Integration
• Operator Traces
• Stochastic Integration
• Scattering Theory
• Random Evolutions
• CLR Inequality
• Operator Equations

Readership: Researchers in measure and integration, functional analysis, operator theory, harmonic analysis, mathematical physics and stochastic processes.
Key Features:

• This book is unique in drawing out the common features of functional analysis in operator traces, scattering theory, stochastic integration, semiclassical approximation and operator equations. The decoupling approach to bilinear integration with respect to vector measures like spectral measures is a common theme of these topics, laid out systematically here for the first time. The background to these topics is described with pointers to the relevant texts so that the book could be used profitably by a graduate student with a knowledge of functional analysis and measure theory or modern mathematical physics