result is known as the Stone–Weierstrass theorem. The Stone–Weierstrass theorem generalizes the Weierstrass approximation theorem in two directions: instead...

theorems are named after Karl Weierstrass. These include: The Weierstrass approximation theorem, of which one well known generalization is the Stone–Weierstrass...

Bolzano–Weierstrass theorem Stone–Weierstrass theorem Casorati–Weierstrass theorem Weierstrass elliptic function Weierstrass function Weierstrass M-test...

theory. The theorem has been the starting point for what is now called Stone duality. In 1937, he published the Stone–Weierstrass theorem which generalized...

certain special polynomials. It is the p-adic counterpart to the Stone-Weierstrass theorem for continuous real-valued functions on a closed interval. Let...

coefficient of the dual representation. Hence the theorem follows directly from the Stone–Weierstrass theorem if the matrix coefficients separate points, which...

f(y).} Separating sets can be used to formulate a version of the Stone–Weierstrass theorem for real-valued functions on a compact Hausdorff space X , {\displaystyle...

,\pi ])} . The density of their span is a consequence of the Stone–Weierstrass theorem, but follows also from the properties of classical kernels like...

). Kolmogorov–Arnold representation theorem Representer theorem No free lunch theorem Stone–Weierstrass theorem Fourier series Hornik, Kurt; Stinchcombe...

Stone's theorem may refer to a number of theorems of Marshall Stone: Stone's representation theorem for Boolean algebras Stone–Weierstrass theorem Stone–von...

Lindemann–Weierstrass theorem Sochocki–Weierstrass theorem Stone–Weierstrass theorem Weierstrass–Enneper parameterization Weierstrass–Erdmann condition Weierstrass approximation...

Silverman–Toeplitz theorem (mathematical analysis) Śleszyński–Pringsheim theorem (continued fraction) Stolz–Cesàro theorem (calculus) Stone–Weierstrass theorem (functional...

countable, so f is zero almost everywhere. In fact, the de Bruijn–Post Theorem states the converse of the above criterion: If f is a function such that...

matrix elements thus separate points, and it then follows from the Stone–Weierstrass theorem that on every compact subset of the group, the matrix elements...

{\displaystyle S^{n-1}} with respect to the uniform topology, by the Stone–Weierstrass theorem. As a result, the sum of these spaces is also dense in the space...

circle, with the uniform norm; this is a special case of the Stone–Weierstrass theorem. More concretely, for every continuous function ⁠ f {\displaystyle...

differentiable functions f {\displaystyle f} by polynomials. By the Stone–Weierstrass theorem, every continuous function on [ a , b ] {\displaystyle [a,b]}...

Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named...

Taylor's theorem, which roughly states that every differentiable function locally looks like a polynomial function, and the Stone–Weierstrass theorem, which...

an elementary consequence of the Stone–Weierstrass theorem (or as a consequence of Weierstrass approximation theorem, because every polynomial is locally...

in the positive real numbers. This is a generalization of the Stone–Weierstrass theorem. Paul Erdős conjectured that all large sets contain arbitrarily...

representation is dense by the Stone–Weierstrass theorem. Conway 1990, Example VII.1.8. Conway 1990, Example VII.1.9. Conway 1990, Theorem VII.2.2. García, Miguel...

{\displaystyle \textstyle \sup _{R}|f|\leq C<\infty } and by the Stone–Weierstrass theorem there exists a sequence of Lipschitz functions f k : R → R {\displaystyle...

Uniform norm Matrix norm Spectral radius Normed division algebra Stone–Weierstrass theorem Banach algebra *-algebra B*-algebra C*-algebra Universal C*-algebra...

fractions; neither includes integrals or limits. Indeed, by the Stone–Weierstrass theorem, any continuous function on the unit interval can be expressed...

Mashreghi–Ransford inequality. He also derived a short elementary proof of Stone–Weierstrass theorem [2]. "Chairholders". chairs-chaires.gc.ca. "The Mathematics Genealogy...

) {\displaystyle (p,0)} -form wherever defined, hence by the Stone–Weierstrass theorem we can write it as β k − β k + 1 ′ = ∑ | I | = p ( P I + r I )...

Bernstein's theorem (approximation theory) Bernstein's theorem on monotone functions Bernstein–von Mises theorem Stone–Weierstrass theorem Youschkevitch...

the Arzelà-Ascoli theorem, the Stone-Weierstrass theorem, Fatou's lemma, and the monotone convergence and dominated convergence theorems. Various ideas from...

Mergelyan's theorem — generalization of Stone–Weierstrass theorem for polynomials Müntz–Szász theorem — variant of Stone–Weierstrass theorem for polynomials...