Science Fair Project Encyclopedia
List of functional analysis topics
This is a list of functional analysis topics, by Wikipedia page.
| Contents |
Hilbert space
- Euclidean space
- Inner product space
- Hilbert space
- Parallelogram law
- Orthonormal basis
- Orthogonalization
- Orthogonal complement
- Gram-Schmidt process
- Legendre polynomials
- Matrices
- Normal vector
- Parseval's identity
- Riesz representation theorem
- Bra-ket notation
- Spectral theorem
- Positive-definite
- Rayleigh quotient
- Mercer's theorem
- Reproducing kernel Hilbert space
- Trace class
- Min-max theorem
- Rigged Hilbert space
- Hellinger-Toeplitz theorem
- Direct integral
- Semi-Hilbert space
Functional analysis, classic results
- Normed vector space
- Banach space
- Hahn-Banach theorem
- Dual space
- Predual
- Weak topology
- Reflexive space
- Polynomially reflexive space
- Baire category theorem
- Open mapping theorem
- Closed graph theorem
- Uniform boundedness principle
- Arzelą-Ascoli theorem
- Banach-Alaoglu theorem
- Measure of non-compactness
Operator theory
- Bounded linear operator
- Spectral theory
- Topologies on the set of operators on a Hilbert space
- norm topology
- ultrastrong topology
- strong operator topology
- weak operator topology
- weak-star operator topology
- ultraweak topology
- S-number
- Fredholm operator
- Fuglede's theorem
- Compression (functional analysis)
- Friedrichs extension
- Stone's theorem on one-parameter unitary groups
- Stone-von Neumann theorem
- Functional calculus
- Hilbert-Polya conjecture
Banach space examples
Real and complex algebras
- Uniform norm
- Matrix norm
- Spectral radius
- Normed division algebra
- Stone-Weierstrass theorem
- Banach algebra
- Star algebra
- B-star-algebra
- C-star-algebra
- Positive element
- Positive linear functional
- operator algebra
- Gelfand representation
- Gelfand-Naimark theorem
- Gelfand-Naimark-Segal construction
- Von Neumann algebra
- von Neumann double commutant theorem
- Topological ring
- Noncommutative geometry
- Disk algebra
- Colombeau algebra
Topological vector spaces
Amenability
Wavelets
- Basis function
- Daubechies wavelet
- Haar wavelet
- Morlet wavelet
- Mexican hat wavelet
- Complex mexican hat wavelet
- Hermitian wavelet
- Hermitian hat wavelet
- Discrete wavelet transform
- Continuous wavelet
- Continuous wavelet transform
Quantum theory
See also list of mathematical topics in quantum theory
- Mathematical formulation of quantum mechanics
- Observable
- Operator (physics)
- Quantum state
- Heisenberg picture
- Density matrix
- Quantum logic
- Quantum operation
- Wightman axioms
Probability
Non-linear
History
- Stefan Banach (1892-1945)
- Hugo Steinhaus (1887-1972)
- John von Neumann
- Alain Connes (born 1947)
12-03-2008 10:22:39
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details