Category:Functional analysis

A

• [+] Approximation theory (17 P)

B

• [+] Banach algebras (3 C, 11 P)

C

• [+] Calculus of variations (4 C, 50 P)

I

• [+] Integral equations (1 C, 7 P)
• [+] Integral transforms (1 C, 43 P)

L

• [+] Linear operators (8 C, 9 P)

M

• [+] Measure theory (5 C, 137 P)

N

• [+] Noncommutative geometry (10 P)
• [+] Nonlinear functional analysis (4 P)

O

• [+] Operator theory (8 C, 95 P)

T

• [+] Topological vector spaces (2 C, 30 P)
• [+] Topology of function spaces (1 C, 20 P)

W

• [+] Wavelets (3 C, 39 P)

• List of functional analysis topics

*

• Functional analysis

A

• Absorbing set
• Analytic Fredholm theorem
• Analytic semigroup
• Antiunitary operator
• Associativity
• Aubin-Lions lemma

B

• Baire category theorem
• Baire space
• Banach limit
• Banach–Alaoglu theorem
• Banach–Mazur theorem
• Bernstein's inequality (mathematical analysis)
• Beta wavelet
• Beta-dual space
• Bochner space
• Bochner's theorem
• Bounded deformation
• Bounded mean oscillation
• Bounded set
• Bred vectors
• Bs space

C

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

D

• Density matrix
• Derivative (generalizations)
• Direct integral
• Dirichlet algebra
• Discontinuous linear map
• Disk algebra
• Distribution (mathematics)
• Dual pair
• Dual space
• Dunford–Schwartz theorem
• Dvoretzky's theorem

E

• Eberlein–Šmulian theorem
• Eigenfunction
• Energetic space
• Extensions of symmetric operators

F

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

G

• Gårding's inequality
• Gelfand representation
• Gelfand–Naimark theorem
• Gelfand–Naimark–Segal construction
• Geometric quantization
• Goldstine theorem
• Gram–Schmidt process
• Grothendieck inequality

H

• Hahn–Banach theorem
• Hamburger moment problem
• Harmonic spectrum
• Hellinger–Toeplitz theorem
• Hille–Yosida theorem
• Hölder's inequality
• Hölder condition

I

• Invariant subspace problem

J

• James' theorem

K

• Kakutani fixed point theorem
• Kantorovich theorem
• Kernel (linear operator)
• Kuratowski embedding

L

• Lauricella's theorem
• Legendre wavelet
• Linear functional
• Lions–Lax–Milgram theorem
• List of Banach spaces
• List of operators
• Lumer-Phillips theorem

M

• M. Riesz extension theorem
• 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
• Müntz–Szász theorem

N

• Negacyclic convolution
• Neumann series

O

• Open mapping theorem (functional analysis)
• Operator algebra
• Ordered vector space
• Orthogonal complement
• Orthogonal functions
• Orthonormal basis

O cont.

• Orthonormality

P

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

Q

• Quasicontraction semigroup
• Quotient of subspace theorem
• Quotient space (linear algebra)

R

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

S

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

T

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

U

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

V

• Volterra series

W

• Wavelet series
• Weak derivative
• Weakly measurable function
• Weierstrass M-test
• Weight function

Z

• Zonal spherical function