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What (who) is Hilbert space - definition
Hilbert space
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![harmonic series]].](https://commons.wikimedia.org/wiki/Special:FilePath/Harmonic partials on strings.svg?width=200 "harmonic series]].")
![[[Spherical harmonics]], an orthonormal basis for the Hilbert space of square-integrable functions on the sphere, shown graphed along the radial direction](https://commons.wikimedia.org/wiki/Special:FilePath/Harmoniki.png?width=200 "[[Spherical harmonics]], an orthonormal basis for the Hilbert space of square-integrable functions on the sphere, shown graphed along the radial direction")
![[[David Hilbert]]](https://commons.wikimedia.org/wiki/Special:FilePath/Hilbert.jpg?width=200 "[[David Hilbert]]")
INNER PRODUCT SPACE THAT IS METRICALLY COMPLETE; A BANACH SPACE WHOSE NORM INDUCES AN INNER PRODUCT (FOLLOWS THE PARALLELOGRAM IDENTITY)
Linear Algebra/Hilbert Spaces; Complex Hilbert space; Hilbert spaces; Hilbert spaces and Fourier analysis; Separable Hilbert space; Complete inner product space; Hilbert Space; Hilbert space dimension; Draft:Xu–Zikatanov identity; Square-summable sequence; ℓ2 space; ℓ2
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an inner product which defines a distance function for which it is a complete metric space.
Hilbert space
INNER PRODUCT SPACE THAT IS METRICALLY COMPLETE; A BANACH SPACE WHOSE NORM INDUCES AN INNER PRODUCT (FOLLOWS THE PARALLELOGRAM IDENTITY)
Linear Algebra/Hilbert Spaces; Complex Hilbert space; Hilbert spaces; Hilbert spaces and Fourier analysis; Separable Hilbert space; Complete inner product space; Hilbert Space; Hilbert space dimension; Draft:Xu–Zikatanov identity; Square-summable sequence; ℓ2 space; ℓ2
¦ noun Mathematics an infinite-dimensional analogue of Euclidean space.
Origin
early 20th cent.: named after the German mathematician David Hilbert.
Rigged Hilbert space
HILBERT SPACE EQUIPPED WITH A DENSE SUBSPACE THAT CARRIES (IN ADDITION TO THE SUBSPACE TOPOLOGY) A FINER TOPOLOGY SUCH THAT THE INCLUSION MAP IS CONTINUOUS
Generalized eigenspaces of unbounded continuous operators; Generalized eigenspaces of unbounded operators; Generalized eigenfunction; Generalised eigenfunction; Gelfand triple; Nested Hilbert space; Equipped Hilbert space; Rigged hilbert space; Banach Gelfand triple; (Banach) Gelfand triple
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. Such spaces were introduced to study spectral theory in the broad sense.
