perturbation

Analytic Perturbation Theory and Its Applications

  • Introduction and Motivation
  • Finite Dimensional Perturbations
  • Inversion of Analytically Perturbed Matrices
  • Perturbation of Null Spaces, Eigenvectors, and Generalized Inverses
  • Polynomial Perturbation of Algebraic Nonlinear Systems
  • Applications to Optimization and Markov Processes
    • Applications to Optimization
    • Applications to Markov Chains
    • Applications to Markov Decision Processes
  • Infinite Dimensional Perturbations
    • Analytic Perturbation of Linear Operators
      • Introduction
      • Preliminaries from Finite Dimensional Theory
      • Key Examples
      • Motivating Applications
      • Review of Banach and Hilbert Spaces
      • Inversion of Linearly Perturbed Operators on Hilbert Spaces
      • Inversion of Linearly Perturbed Operators on Banach Spaces
      • Polynomial and Analytic Perturbations
      • Problems
    • Background on Hilbert Spaces and Fourier Analysis**
      • The Hilbert Space L2([−π,π])
      • The Fourier Series Representation on ([−π,π])
      • Fourier Series Representation on L2([−π,π])
      • The Space l2 .
      • The Hilbert Space H1 0 ([−π,π])
      • Fourier Integrals in H1 (R)
      • The Complex Hilbert Space L2(R)
      • Fourier Integrals in the Complex Space L2(R)