Concept information
Término preferido
functional analysis
Definición
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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)
Concepto genérico
Conceptos específicos
- 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
- function space
- functional
- geometry of numbers
- Grothendieck trace theorem
- Hahn-Banach theorem
- Hilbert projection theorem
- integro-differential equation
- Korn's inequality
- Krein-Milman theorem
- M. Riesz extension theorem
- Minkowski functional
- 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
En otras lenguas
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francés
URI
http://data.loterre.fr/ark:/67375/PSR-HX2VX066-P
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