Concept information
Preferred term
functional analysis
Definition
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Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous or unitary operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Functional_analysis)
Broader concept
Narrower concepts
- approximation theory
- Banach algebra
- Banach-Stone theorem
- Bessel's inequality
- bipolar theorem
- calculus of variations
- Carleson measure
- completely positive map
- convolution
- distribution
- Fourier series
- fractional calculus
- functional
- function space
- geometry of numbers
- Grothendieck trace theorem
- Hahn-Banach theorem
- Hilbert projection theorem
- integro-differential equation
- Korn's inequality
- Krein-Milman theorem
- Minkowski functional
- M. Riesz extension theorem
- operator
- operator algebra
- Parseval's identity
- polar set
- relative interior
- Riesz-Thorin theorem
- Schur's theorem
- singular value decomposition
- special function
- spectral theory
- strictly convex space
- sublinear function
- supporting hyperplane
- transformation
- uniform convergence
- uniformly convex space
- von Neumann bicommutant theorem
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-HX2VX066-P
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