In mathematics, Bochner's theorem (named for Salomon Bochner) characterizes the Fourier transform of a positive finite Borel measure on the real line....

quantified utilizing Bochner's theorem. The name Nyquist–Shannon sampling theorem honours Harry Nyquist and Claude Shannon, but the theorem was also previously...

function g on the real line with g(y) ≥ 0. The converse result is Bochner's theorem, stating that any continuous positive-definite function on the real...

In mathematics, Bochner's tube theorem (named for Salomon Bochner) shows that every function holomorphic on a tube domain in C n {\displaystyle \mathbb...

arguments. In 1933 he defined the Bochner integral, as it is now called, for vector-valued functions. Bochner's theorem on Fourier transforms appeared in...

at infinity, i.e., the Riemann–Lebesgue lemma fails for measures. Bochner's theorem characterizes which functions may arise as the Fourier–Stieltjes transform...

Consequently the isometry group of the manifold must be finite. The theorem is a corollary of Bochner's more fundamental result which says that on any connected...

x , y ) = K ( x − y ) {\displaystyle K(x,y)=K(x-y)} ) is given by Bochner's theorem. It states that a continuous function K ( x − y ) {\displaystyle K(x-y)}...

The central result here is Bochner’s theorem, although its usefulness is limited because the main condition of the theorem, non-negative definiteness...

of the Lebesgue integral continue to hold for the Bochner integral. Particularly useful is Bochner's criterion for integrability, which states that if...

In mathematics, Bochner's formula is a statement relating harmonic functions on a Riemannian manifold ( M , g ) {\displaystyle (M,g)} to the Ricci curvature...

v〉 where Ug is a (strongly continuous) unitary representation (see Bochner's theorem). Replacing v, a rank-1 projection, by a general projection gives...

}a_{m-n}\lambda _{m}{\overline {\lambda _{n}}}=2(1-|z|^{2})\,\Re \,f(z).} Bochner's theorem Carathéodory, C. (1907), "Über den Variabilitätsbereich der Koeffizienten...

functional on a nuclear space A , {\displaystyle A,} the Bochner–Minlos theorem (after Salomon Bochner and Robert Adol'fovich Minlos) guarantees the existence...

positive definiteness of the autocovariance function, it follows from Bochner's theorem that there exists a positive measure μ {\displaystyle \mu } on the...

stronger convergence guarantee by Hoeffding's inequality.: Claim 1  By Bochner's theorem, the above construction can be generalized to arbitrary positive definite...

instead of functions. If R x x {\displaystyle R_{xx}} is continuous, Bochner's theorem can be used to prove that its Fourier transform exists as a positive...

mathematical theory of artificial neural networks, universal approximation theorems are theorems of the following form: Given a family of neural networks, for each...

can be finished by using Bochner's formula to construct parallel vector fields, setting up the de Rham decomposition theorem. Alternatively, the theory...

single-argument version of the covariance function can be checked by Bochner's theorem. For a given variance σ 2 {\displaystyle \sigma ^{2}} , a simple stationary...

of envelope of topological algebra. Peter–Weyl theorem Cartier duality Stereotype space Bochner's theorem Joint continuousness means here that the map G...

geometry) Bochner's tube theorem (complex analysis) Cartan's theorems A and B (several complex variables) Castelnuovo–de Franchis theorem (algebraic...

design Blocking (statistics) Blumenthal's zero–one law BMDP – software Bochner's theorem Bonferroni correction Bonferroni inequalities – redirects to Boole's...

theory of functions of several complex variables, Hartogs's extension theorem is a statement about the singularities of holomorphic functions of several...

Two theorems in the mathematical field of Riemannian geometry bear the name Myers–Steenrod theorem, both from a 1939 paper by Myers and Steenrod. The first...

Bochner's theorem Hamburger moment problem Moment problem Orthogonal polynomials on the unit circle Spectral measure Schur class Szegő limit theorems...

In mathematics, the closed-subgroup theorem (sometimes referred to as Cartan's theorem) is a theorem in the theory of Lie groups. It states that if H is...

x')=h(x-x')} with x ∈ R b {\displaystyle x\in \mathbb {R} ^{b}} . Then Bochner's theorem guarantees the existence of a unique finite Borel measure μ {\displaystyle...

Parseval–Gutzmer formula Bochner–Martinelli formula Helffer–Sjöstrand formula Titchmarsh 1939, p. 84 "Gauss's Mean-Value Theorem". Wolfram Alpha Site. Pompeiu...

to Z×Z. Myers theorem. If a complete Riemannian manifold has positive Ricci curvature then its fundamental group is finite. Bochner's formula. If a compact...