and Hilbert space theory, the fundamental theorem of Hilbert spaces gives a necessary and sufficient condition for a Hausdorff pre-Hilbert space to be...

plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is a vector space equipped with an inner product...

There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information...

Euclidean space Fundamental theorem of Hilbert spaces Gram–Schmidt process Hellinger–Toeplitz theorem Hilbert space Inner product space Legendre polynomials...

also an injective isometry. The Fundamental theorem of Hilbert spaces, which is related to Riesz representation theorem, states that this map is surjective...

which the spectral theorem applies are self-adjoint operators or more generally normal operators on Hilbert spaces. The spectral theorem also provides a...

In mathematical analysis, the Hilbert–Schmidt theorem, also known as the eigenfunction expansion theorem, is a fundamental result concerning compact, self-adjoint...

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

"Banach space" and Banach in turn then coined the term "Fréchet space". Banach spaces originally grew out of the study of function spaces by Hilbert, Fréchet...

mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental ideas including invariant...

mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states...

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...

of topological vector spaces, which include function spaces, inner product spaces, normed spaces, Hilbert spaces and Banach spaces. In this article, vectors...

representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is fundamental to the deeper...

the proof of results in many areas of analysis and geometry, including some of the fundamental theorems of functional analysis. Versions of the Baire...

Wigner's theorem states a converse of the above: Wigner's theorem (1931)—If H {\displaystyle H} and K {\displaystyle K} are Hilbert spaces and if T :...

non-self-intersecting curves of nonzero area, the Osgood curves, but by Netto's theorem they are not space-filling. For the classic Peano and Hilbert space-filling curves...

kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Specifically, a Hilbert space H {\displaystyle...

the theory of integral equations; it is used in the Hilbert space theory of stochastic processes, for example the Karhunen–Loève theorem; and it is also...

great innovation of proving all properties of the space as theorems, by starting from a few fundamental properties, called postulates, which either were...

of derivatives and integrals in alternative calculi List of equations List of fundamental theorems List of hypotheses List of inequalities Lists of integrals...

In mathematics, a Hilbert–Schmidt integral operator is a type of integral transform. Specifically, given a domain Ω in Rn, any k : Ω × Ω → C such that...

mathematics, Hilbert's syzygy theorem is one of the three fundamental theorems about polynomial rings over fields, first proved by David Hilbert in 1890,...

half-planes in the Hardy space H2 by the Paley–Wiener theorem. Formally, the derivative of the Hilbert transform is the Hilbert transform of the derivative, i...

In differential geometry, Hilbert's theorem (1901) states that there exists no complete regular surface S {\displaystyle S} of constant negative gaussian...

environment Hilbert space in accordance with the no-hiding theorem. This experiment for the first time demonstrated the conservation of quantum information...

in Hilbert space only up to a phase factor i.e. as an element of projectivised Hilbert space. To prove the theorem, we select an arbitrary pair of states...

infinite-dimensional spaces are of central importance in these fields. Sazonov's theorem also has a converse: if the map is not Hilbert–Schmidt, then it is...

theorem from spaces of geometrical points to spaces of functions. The Arzelà–Ascoli theorem and the Peano existence theorem exemplify applications of...

mathematics, Hilbert's Nullstellensatz (German for "theorem of zeros", or more literally, "zero-locus-theorem") is a theorem that establishes a fundamental relationship...