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Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of spaces of functions. It has its historical roots in the study of transformations, such as the Fourier transform, and in the study of differential and integral equations. This usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function. Its use in general has been attributed to mathematician and physicist Vito Volterra and its founding is largely attributed to mathematician Stefan Banach.
Normed vector spaces
In the modern view, functional analysis is seen as the study of complete normed vector spaces over the real or complex numbers. Such spaces are called Banach spaces. An important example is a Hilbert space, where the norm arises from an inner product. These spaces are of fundamental importance in many areas, including the mathematical formulation of quantum mechanics. More generally, functional analysis includes the study of Fréchet spaces and other topological vector spaces not endowed with a norm.
An important object of study in functional analysis are the continuous linear operators defined on Banach and Hilbert spaces. These lead naturally to the definition of C*-algebras and other operator algebras.
More on [ Functional analysis ]
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Banach Algebra Resources - Links of interest in Banach algebras and related areas (operator theory, abstract harmonic analysis, C*-algebras, and operator spaces). Maintained by Volker Runde.
Counterexamples in Functional Analysis - A collection of examples in functional analysis and operator theory.
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Functional Analysis - Preprints in the ArXiv.
Functional Analysis - In the Mathematical Atlas.
Functional Analysis Seminar - Web page of the functional analysis seminar at the University of Alberta
Funktionalanalysis - Institut für Analysis, Johannes Kepler Universität Linz, Austria. Seminar, publications, staff.
Meta Description: [ Homepage of Gruppe Funktionalanalysis,
(Functional analysis group), University Linz ]
Geometric Functional Analysis at Penn State - Seminar; Courses; Meetings; People ; Links.
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Ghent Research Group for Numerical Functional Analysis and Mathematical Modeling - Includes focus of studies, list of staff and preprints. In Belgium.
Hilbert C*-Modules Home Page - Bibliographies on Hilbert C*-module theory.
Meta Description: [ Hilbert C*-modules home page, Leipzig, Germany ]
Hilbert's Moment Problem - A result strongly suggested by computer data but no proof has been found.
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Journal of Functional Analysis - Academic Press.
Mathematics Research at Lancaster University - Including operator algebras, Banach spaces and K-theory.
North British Functional Analysis Seminar (NBFAS) - NBFAS normally meets three times per year, holding a one- or two-day meeting in one of its member institutions at which distinguished mathematicians are invited to lecture.
Operator Algebra Resources - Links, directories, pulciations and events; maintained by N. Christopher Phillips.
Operator Algebraist's Information Stack - Leipzig - Information desk for operator algebraists: Leipzig, Germany.
Meta Description: [ Homepage of Operator Algebraists, Leipzig, Germany ]
Operator Algebras Home Page - Links, publications, research groups. Maintained by Birant Ramazan.
Oxford Functional Analysis Group - The interests of the group are diverse ranging from topological aspects of the geometry of Banach spaces, through operator systems, to topics bordering on probability and differential equations.
Seminar on Functional Analysis and Applications - Supported by Centro de Matemática Aplicada and PRAXIS XXI, Lisbon.
| , inner product induced metric. Parallelogram law, Cauchy Swartz, any two norms on a finite dimensional space are ... | |
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