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37 relations: Alexander Grothendieck, Balanced set, Banach space, Barrelled space, Cambridge University Press, Closed manifold, Cylinder set measure, Distribution (mathematics), Dual space, Fourier inversion theorem, Fréchet space, Fredholm kernel, Graduate Texts in Mathematics, Heine–Borel theorem, Hilbert space, Hilbert–Schmidt operator, Locally convex topological vector space, Mathematics, Montel space, Norm (mathematics), Nuclear operator, Probability measure, Radon measure, Random element, Randomness, Rigged Hilbert space, Robert Minlos, Salomon Bochner, Schwartz space, Smoothness, Springer Science+Business Media, Subbase, Topological tensor product, Topological vector space, Trace class, Vector space, White noise.
Alexander Grothendieck
Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry.
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Balanced set
In linear algebra and related areas of mathematics a balanced set, circled set or disk in a vector space (over a field K with an absolute value function |\cdot |) is a set S such that for all scalars \alpha with |\alpha| \leqslant 1 where The balanced hull or balanced envelope for a set S is the smallest balanced set containing S. It can be constructed as the intersection of all balanced sets containing S.
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Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
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Barrelled space
In functional analysis and related areas of mathematics, barrelled spaces are Hausdorff topological vector spaces for which every barrelled set in the space is a neighbourhood for the zero vector.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Closed manifold
In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary.
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Cylinder set measure
In mathematics, cylinder set measure (or promeasure, or premeasure, or quasi-measure, or CSM) is a kind of prototype for a measure on an infinite-dimensional vector space.
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Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
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Dual space
In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.
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Fourier inversion theorem
In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform.
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Fréchet space
In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces.
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Fredholm kernel
In mathematics, a Fredholm kernel is a certain type of a kernel on a Banach space, associated with nuclear operators on the Banach space.
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Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.
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Heine–Borel theorem
In real analysis the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states: For a subset S of Euclidean space Rn, the following two statements are equivalent.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Hilbert–Schmidt operator
In mathematics, a Hilbert–Schmidt operator, named for David Hilbert and Erhard Schmidt, is a bounded operator A on a Hilbert space H with finite Hilbert–Schmidt norm where \|\ \| is the norm of H, \ an orthonormal basis of H, and Tr is the trace of a nonnegative self-adjoint operator.
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Locally convex topological vector space
In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Montel space
In functional analysis and related areas of mathematics, a Montel space, named after Paul Montel, is any topological vector space in which an analog of Montel's theorem holds.
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Nuclear operator
In mathematics, a nuclear operator is a compact operator for which a trace may be defined, such that the trace is finite and independent of the choice of basis (at least on well behaved spaces; there are some spaces on which nuclear operators do not have a trace).
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Probability measure
In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity.
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Radon measure
In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular.
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Random element
In probability theory, random element is a generalization of the concept of random variable to more complicated spaces than the simple real line.
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Randomness
Randomness is the lack of pattern or predictability in events.
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Rigged Hilbert space
In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square-integrable aspects of functional analysis.
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Robert Minlos
Robert Adol'fovich Minlos (Роберт Адольфович Минлос; 28 February 1931 – 9 January 2018) was a Soviet and Russian mathematician who has made important contributions to probability theory and mathematical physics.
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Salomon Bochner
Salomon Bochner (20 August 1899 – 2 May 1982) was an American mathematician, known for work in mathematical analysis, probability theory and differential geometry.
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Schwartz space
In mathematics, Schwartz space is the function space of all functions whose derivatives are rapidly decreasing (defined rigorously below).
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Subbase
In topology, a subbase (or subbasis) for a topological space with topology is a subcollection of that generates, in the sense that is the smallest topology containing.
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Topological tensor product
In mathematics, there are usually many different ways to construct a topological tensor product of two topological vector spaces.
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Topological vector space
In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.
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Trace class
In mathematics, a trace class operator is a compact operator for which a trace may be defined, such that the trace is finite and independent of the choice of basis.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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White noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.
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Redirects here:
Bochner-Minlos theorem, Bochner–Minlos theorem, Nuclear spaces, Nuclearity, White noise measure.
References
[1] https://en.wikipedia.org/wiki/Nuclear_space
