Applied Linear Operators and Spectral Methods

Banach and Normed Spaces Hilbert Spaces and Orthogonality Orthonormal Bases and Total Sets Bounded Linear Operators Adjoint Operators and Riesz Representation Self-Adjoint and Positive Operators Compact Operators Finite Rank Operators and Approximation Fredholm Alternative Spectral Theory of Operators Point, Continuous, and Residual Spectrum Resolvent Sets and Spectral Bounds Shift and Multiplication Operators Sequence Spaces Operator Topologies and Strong Convergence Dual Spaces and Bounded Linear Functionals Hahn-Banach Theorem Separation Theorems and Supporting Hyperplanes Convex Sets and Projection Theorems Contraction Mapping and Nonlinear Equations Fourier Transform and Sampling Theory