TL;DR: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of algebraic stability analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Method as discussed by the authors.
Abstract: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of Algebraic Stability Analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Methods Numerical Results for Hyperbolic Problems Advection-Diffusion Equation Models of Incompressible Fluid Dynamics Miscellaneous Applications of Spectral Methods Survey of Spectral Methods and Applications Properties of Chebyshev and Legendre Polynomial Expansions.
TL;DR: In this article, the spectrum and spectral inclusions for multipliers are discussed. But they do not cover the connection between automatic continuity and functional models, duality theory, and invariant subspaces.
Abstract: 1 Decomposable operators 2 Functional models, duality theory, and invariant subspaces 3 The spectrum and spectral inclusions 4 Local spectral theory for multipliers 5 Connections to automatic continuity 6 Open problems Appendix Bibliography Index of notation Index