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...

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

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...

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...

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

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

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...

{\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...

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...

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

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

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

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

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

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...

{\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...

with Richard Anthony Rasala and William C. Waterhouse: The Stone-Weierstrass theorem for valuable fields Pacific Journal of Mathematics vol. 27, no...

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

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

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

the Gibbs phenomenon in Fourier series approximations. The Weierstrass approximation theorem states that for every continuous function f ( x ) {\displaystyle...

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...

and the supremum in the above definition is attained by the Weierstrass extreme value theorem, so we can replace the supremum by the maximum. In this case...

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

subsequence that converges to some point of the space. The Bolzano–Weierstrass theorem states that a subset of Euclidean space is compact in this sequential...

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...