Category:Functional analysis

A

• Approximation theory (1 C, 17 P)

B

• Banach algebras (3 C, 12 P)

C

• Calculus of variations (5 C, 51 P)

I

• Integral equations (1 C, 7 P)
• Integral transforms (1 C, 42 P)

N

• Nonlinear functional analysis (5 P)

O

• Operator theory (6 C, 101 P)

T

• Topological vector spaces (2 C, 41 P)
• Topology of function spaces (18 P)

W

• Wavelets (3 C, 37 P)

• Functional analysis

*

• List of functional analysis topics

A

• Absorbing set
• Action selection
• Analytic semigroup
• Antiunitary operator
• Associative property

B

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

C

• C space
• C*-algebra
• C0-semigroup
• CCR and CAR algebras
• Choquet integral
• Choquet theory
• Circular convolution
• Coercive function
• Colombeau algebra
• Commutative property
• Compact convergence
• Compact embedding
• Complementarity theory
• Compression (functional analysis)
• Conjugate index
• Constructive quantum field theory
• Continuous embedding
• Continuous linear extension
• Continuous linear operator
• Convolution
• Convolution power
• Current (mathematics)

D

• Degenerate bilinear form
• Densely defined operator
• Density matrix
• Direct integral
• Dirichlet algebra
• Discontinuous linear map
• Discretization
• Disk algebra
• Distribution (mathematical analysis)
• Distribution (mathematics)
• Dual norm
• Dual space

E

• Eigenfunction
• Energetic space
• Extensions of symmetric operators
• Extreme point

F

• Free probability
• Functional determinant
• Functional integration
• Functional square root

G

• Gelfand representation
• Gelfand–Naimark–Segal construction
• Geometric quantization
• Gram–Schmidt process

H

• Hadamard space
• Hamburger moment problem
• Harmonic spectrum
• Hölder condition

I

• Infinite-dimensional optimization
• Invariant subspace problem

K

• Kantorovich theorem
• Kernel (linear algebra)

L

• Linear form
• Linear subspace
• Local boundedness
• Locally compact quantum group
• Locally convex topological vector space

M

• Measure of non-compactness
• Minkowski functional
• Mollifier
• Monotonic function
• Montel space
• Müntz–Szász theorem

N

• Negacyclic convolution
• Neumann series
• Norm (mathematics)

O

• Operator (mathematics)
• Operator algebra
• Operator norm
• Operator topologies
• List of mathematic operators
• Order dual (functional analysis)
• Ordered vector space
• Orthogonal basis
• Orthogonal complement
• Orthogonal functions
• Orthonormal basis
• Orthonormal function system
• Orthonormality
• Oscillatory integral

P

• Partial trace
• Peetre's inequality
• Perturbation theory
• Polar set
• Polarization identity
• Positive linear functional
• Predual
• Prevalent and shy sets
• Projection (linear algebra)
• Pseudo-differential operator

Q

• Quasicontraction semigroup
• Quotient space (linear algebra)

R

• Riesz sequence
• Riesz space
• Riesz's lemma

S

• Sequence space
• Sesquilinear form
• Singular value decomposition
• Space of continuous functions on a compact space
• Spectral set
• Spectral theory of compact operators
• Spectrum of a ring
• Star domain
• State (functional analysis)
• Stone–von Neumann theorem
• Strongly positive bilinear form
• Sublinear function
• Supporting hyperplane
• Symmetric convolution
• System of imprimitivity

T

• Tensor product of Hilbert spaces
• Totally bounded space
• Transpose of a linear map
• Trigonometric moment problem

U

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

V

• Vector measure
• Volterra series

W

• Wavelet transform
• Weak derivative
• Weakly measurable function
• Weierstrass M-test
• Weight function
• Weighted space

Z

• Zonal spherical function