List of functional analysis topics
This is a list of functional analysis topics, by Wikipedia page.
| Table of contents |
|
2 Functional analysis, classic results 3 Real and complex algebrass 4 Topological vector spaces 5 Wavelets 6 Quantum theory 7 History |
Hilbert space
- Euclidean space
- Inner product space
- Hilbert space
- Orthonormal basis
- Orthogonalization
- Gram-Schmidt process
- Legendre polynomials
- Matrices
- Normal vector
- Riesz representation theorem
- Bra-ket notation
- Spectral theorem
- Positive-definite
- Rayleigh quotient
- Mercer's theorem
- Trace class
Functional analysis, classic results
- Normed vector space
- Bounded linear operator
- Banach space
- Hahn-Banach theorem
- Dual space
- Weak topology
- Reflexive space
- Baire category theorem
- Open mapping theorem
- Closed graph theorem
- Uniform boundedness principle
- Fredholm operator
Real and complex algebrass
- Stone-Weierstrass theorem
- Banach algebra
- B-star-algebra
- C-star algebra
- Gelfand representation
- Gelfand-Naimark-Segal
- Von Neumann algebra
- Topological ring
- Noncommutative geometry
- Colombeau algebra
Topological vector spaces
- Frechet space
- F-space
Wavelets
Quantum theory
- Mathematical formulation of quantum mechanics
- Quantum state
- Heisenberg picture
- Density matrix
- Wightman axioms
History
- Stefan Banach (1892-1945)
- Hugo Steinhaus (1887-1972)
- Alain Connes (born 1947)
