Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Functional_analysis> ?p ?o }
- Functional_analysis abstract "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 (e.g. inner product, norm, topology, etc.) and the linear operators acting upon these spaces and respecting these structures in a suitable sense. 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 continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations.The usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function and the name was first used in Hadamard's 1910 book on that subject. However, the general concept of a functional had previously been introduced in 1887 by the Italian mathematician and physicist Vito Volterra. The theory of nonlinear functionals was continued by students of Hadamard, in particular Fréchet and Lévy. Hadamard also founded the modern school of linear functional analysis further developed by Riesz and the group of Polish mathematicians around Stefan Banach.In modern introductory texts to functional analysis, the subject is seen as the study of vector spaces endowed with a topology, in particular infinite-dimensional spaces. In contrast, linear algebra deals mostly with finite-dimensional spaces, and does not use topology. An important part of functional analysis is the extension of the theory of measure, integration, and probability to infinite dimensional spaces, also known as infinite dimensional analysis.".
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- Functional_analysis wikiPageExternalLink index.html.
- Functional_analysis wikiPageExternalLink www.coursera.org.
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- Functional_analysis wikiPageExternalLink Theory-of-Linear-Operations--Volume-38--North-Holland-Mathematical-Library--by-S--Banach_134628.html.
- Functional_analysis wikiPageExternalLink Calculus%20and%20Analysis%20Earliest%20Uses.htm.
- Functional_analysis wikiPageExternalLink Functional_Analysis.pdf.
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- Functional_analysis wikiPageWikiLink Basis_(linear_algebra).
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- Functional_analysis wikiPageWikiLink Law_of_large_numbers.
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- Functional_analysis wikiPageWikiLink Lwów_School_of_Mathematics.
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- Functional_analysis wikiPageWikiLink Mathematical_formulation_of_quantum_mechanics.
- Functional_analysis wikiPageWikiLink Mathematical_physics.
- Functional_analysis wikiPageWikiLink Maurice_René_Fréchet.