Introduction
Spaces of Test Functions
Schwartz Distributions
Calculus for Distributions
Distributions as Derivatives of Functions
Tensor Products
Convolution Products
Applications of Convolution
Holomorphic Functions
Fourier Transformations
Distributions as Boundary Values of Analytic Functions
Other Spaces of Generalized Functions
Sobolev Spaces
Hilbert Spaces: A Brief Historical Introduction
Inner Product Spaces and Hilbert Spaces
Geometry of Hilbert Spaces
Separable Hilbert Spaces
Direct Sums and Tensor Products
Topological Aspects
Linear Operators
Quadratic Forms
Bounded Linear Operators
Special Classes of Linear Operators
Elements of Spectral Theory
Compact Operators
Hilbert-Schmidt and Trace Class Operators
The Spectral Theorem
Some Applications of the Spectral Representation
Spectral Analysis in Rigged Hilbert Spaces
Operator Algebras and Positive Mappings
Positive Mappings in Quantum Physics
Introduction
Direct Methods in the Calculus of Variations
Differential Calculus on Banach Spaces and Extrema of Functions
Constrained Minimization Problems (Method of Lagrange Multipliers)
Boundary and Eigenvalue Problems
Density Functional Theory of Atoms and Molecules
Appendices
Index.