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Triebel–Lizorkin Space
In the mathematical discipline known as functional analysis, a Triebel–Lizorkin space is a generalization of many standard function spaces such as ''L''''p'' spaces and Sobolev spaces. It is named after (born February 7th 1936 in Dessau Dessau is a town and former municipality in Germany at the confluence of the rivers Mulde and Elbe, in the '' Bundesland'' (Federal State) of Saxony-Anhalt. Since 1 July 2007, it has been part of the newly created municipality of Dessau-Roßlau ...) and . External links Homogeneity Property of Besov and Triebel-Lizorkin Spaces References *. * Functional analysis {{Mathanalysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
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 space#Definition, inner product, Norm (mathematics)#Definition, norm, Topological space#Definition, topology, etc.) and the linear transformation, linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous function, continuous, unitary operator, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of variati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lp Space
In mathematics, the spaces are function spaces defined using a natural generalization of the Norm (mathematics)#p-norm, -norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue , although according to the Nicolas Bourbaki, Bourbaki group they were first introduced by Frigyes Riesz . spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of their key role in the mathematical analysis of measure and probability spaces, Lebesgue spaces are used also in the theoretical discussion of problems in physics, statistics, economics, finance, engineering, and other disciplines. Applications Statistics In statistics, measures of central tendency and statistical dispersion, such as the mean, median, and standard deviation, are defined in terms of metrics, and measures of central tendency can be characterized as Central tendency#Solutions to variational problems, solutions to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sobolev Space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, i.e. a Banach space. Intuitively, a Sobolev space is a space of functions possessing sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and regularity of a function. Sobolev spaces are named after the Russian mathematician Sergei Sobolev. Their importance comes from the fact that weak solutions of some important partial differential equations exist in appropriate Sobolev spaces, even when there are no strong solutions in spaces of continuous functions with the derivatives understood in the classical sense. Motivation In this section and throughout the article \Omega is an open subset of \R^n. There are many c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dessau
Dessau is a town and former municipality in Germany at the confluence of the rivers Mulde and Elbe, in the '' Bundesland'' (Federal State) of Saxony-Anhalt. Since 1 July 2007, it has been part of the newly created municipality of Dessau-Roßlau. Population of Dessau proper: 67,747 (Dec. 2020). Geography Dessau is situated on a floodplain where the Mulde flows into the Elbe. This causes yearly floods. The worst flood took place in the year 2002, when the Waldersee district was nearly completely flooded. The south of Dessau touches a well-wooded area called Mosigkauer Heide. The highest elevation is a 110 m high former rubbish dump called Scherbelberg in the southwest of Dessau. Dessau is surrounded by numerous parks and palaces that make it one of the greenest towns in Germany. History Dessau was first mentioned in 1213. It became an important centre in 1570, when the Principality of Anhalt was founded. Dessau became the capital of this state within the Holy Roman Empire. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
