Category:Functional analysis

• ► Theorems in functional analysis‎ (76 P)

A

• ► Approximation theory‎ (1 C, 27 P)

B

• ► Banach algebras‎ (3 C, 16 P)

C

• ► Calculus of variations‎ (7 C, 58 P)
• ► Convex hulls‎ (2 C, 14 P)

F

• ► F-spaces‎ (2 C, 1 P)
• ► Function spaces‎ (1 C, 5 P)
• ► Functional analysts‎ (4 C, 50 P)

I

• ► Integral equations‎ (1 C, 8 P)
• ► Integral representations‎ (1 C, 6 P)
• ► Integral transforms‎ (1 C, 44 P)

L

• ► Linear operators‎ (7 C, 7 P)

M

• ► Metric linear spaces‎ (1 C)
• ► Metric spaces‎ (1 C)

N

• ► Noncommutative geometry‎ (10 P)
• ► Nonlinear functional analysis‎ (4 P)

O

• ► Operator theory‎ (10 C, 116 P)
• ► Optimization in vector spaces‎ (2 C, 6 P)

S

• ► Sequence spaces‎ (1 P)

T

• ► Topological vector spaces‎ (3 C, 30 P)
• ► Topology of function spaces‎ (1 C, 21 P)

V

• ► Variational analysis‎ (5 C, 10 P)

W

• ► Wavelets‎ (3 C, 42 P)

• Functional analysis
• List of functional analysis topics

*

• Bounded mean oscillation

A

• Absorbing set
• Analytic semigroup
• Antiunitary operator
• Approximation property
• Asplund space
• Associative property
• Aubin–Lions lemma

B

• Baire category theorem
• Baire space
• Banach limit
• Banach–Alaoglu theorem
• Banach–Mazur compactum
• Banach–Mazur theorem
• Barrier cone
• Beppo-Levi space
• Bernstein's inequality (mathematical analysis)
• Beta wavelet
• Beta-dual space
• Bochner measurable function
• Bochner space
• Bounded deformation
• Bounded set
• Bred vector
• Bs space

C

• C space
• C0-semigroup
• Cauchy–Rassias stability
• CCR and CAR algebras
• Choquet integral
• Choquet theory
• Christoffel–Darboux formula
• Circular convolution
• Closed graph theorem
• Closed range theorem
• Coercive function
• Colombeau algebra
• Commutative property
• Compact convergence
• Compactly embedded
• Complementarity theory
• Composition operator
• Compression (functional analysis)
• Conjugate index
• Constructive quantum field theory
• Continuous functions on a compact Hausdorff space
• Continuous linear extension
• Continuous linear operator
• Continuous wavelet
• Continuously embedded
• Convolution
• Convolution power
• Cylindrical σ-algebra

D

• Density matrix
• Direct integral
• Dirichlet algebra
• Dirichlet space
• Discontinuous linear map
• Discretization
• Disk algebra
• Distortion problem
• Distribution (mathematics)
• Dual pair
• Dual space
• Dunford–Schwartz theorem

D cont.

• Dvoretzky's theorem

E

• Eberlein–Šmulian theorem
• Eigenfunction
• Ekeland's variational principle
• Energetic space
• Extensions of symmetric operators
• Extreme point

F

• F-space
• Fixed-point theorems in infinite-dimensional spaces
• Free convolution
• Free independence
• Free Poisson distribution
• Free probability
• Functional determinant
• Functional integration
• Functional square root

G

• Gårding's inequality
• Gelfand representation
• Gelfand–Naimark theorem
• Gelfand–Naimark–Segal construction
• Gelfand–Shilov space
• Generalizations of the derivative
• Geometric quantization
• Goldstine theorem
• Gram–Schmidt process
• Grothendieck inequality

H

• Hahn–Banach theorem
• Hamburger moment problem
• Harmonic spectrum
• Hellinger–Toeplitz theorem
• Helly space
• Helmut H. Schaefer
• High-dimensional statistics
• Hille–Yosida theorem
• Hölder condition
• Hölder's inequality
• Hyers–Ulam–Rassias stability
• Hypercyclic operator

I

• Infinite-dimensional optimization
• Invariant subspace problem

J

• James' theorem

K

• Kakutani fixed-point theorem
• Kantorovich theorem
• Kernel (linear operator)
• User:Kiefer.Wolfowitz/Sandbox
• Krein–Rutman theorem
• Kuratowski embedding

L

• Lauricella's theorem
• Legendre wavelet
• Linear functional
• Linear subspace
• Lions–Lax–Milgram theorem
• List of Banach spaces
• List of operators
• Lumer–Phillips theorem
• Lyapunov vector
• Lyapunov–Schmidt reduction

M

• Marcinkiewicz interpolation theorem
• Mazur's lemma
• Measure of non-compactness
• Mercer's theorem
• Min-max theorem
• Minkowski functional
• Minlos' theorem
• Mollifier
• Monotonic function
• Multiplication operator

M cont.

• Müntz–Szász theorem

N

• Negacyclic convolution
• Neumann series

O

• Open mapping theorem (functional analysis)
• Operator (mathematics)
• Operator algebra
• Ordered vector space
• Orlicz–Pettis theorem
• Orthogonal complement
• Orthogonal functions
• Orthonormal basis
• Orthonormal function system
• Orthonormality

P

• Parseval's identity
• Partial trace
• Partially defined operator
• Peetre theorem
• Perturbation theory
• Pettis integral
• Polar set
• Polarization identity
• Positive element
• Positive linear functional
• Predual
• Projection (linear algebra)
• Pseudo-differential operator

Q

• Square-integrable function
• Quasicontraction semigroup
• Quotient of subspace theorem
• Quotient space (linear algebra)

R

• Radon–Riesz property
• Riesz sequence
• Riesz space
• Riesz' lemma
• Ryll-Nardzewski fixed-point theorem

S

• Sazonov's theorem
• Schauder fixed point theorem
• Schur's property
• Semi-inner-product
• Sequence space
• Sesquilinear form
• Shannon wavelet
• Singular value decomposition
• Spectral set
• Spectral theory of compact operators
• Spectrum continuation analysis
• Spherically complete field
• State (functional analysis)
• Stone's theorem on one-parameter unitary groups
• Strongly positive bilinear form
• Supporting functional
• Supporting hyperplane
• Symmetric convolution
• System of imprimitivity

T

• T(1) theorem
• Tensor product of Hilbert spaces
• Tonelli's theorem (functional analysis)
• Triebel–Lizorkin space
• Trigonometric moment problem

U

• Uniform algebra
• Uniform boundedness principle
• Uniform norm
• Uniformly Cauchy sequence
• Unit sphere
• Unitary transformation

V

• Vector measure