Question

If $p$ is a polynomial approximating a continuous function $h$, why can we assume $\left\|p\right\|_\infty\le\left\|h\right\|_\infty$?

score 42 · Answer 1 · 2026-04-04 07:13:36

42

Views

If $p$ is a polynomial approximating a continuous function $h$, why can we assume $\left\|p\right\|_\infty\le\left\|h\right\|_\infty$?

Published on 04 Apr 2026 - 7:13

score 64 · Answer 2 · 2026-04-05 07:02:16

64

Views

Inequality of expectation in Weierstrass theorem

Published on 05 Apr 2026 - 7:02

score 87 · Answer 3 · 2026-04-03 21:28:26

87

Views

What does the phrase "by a polynomial in a finite number of functions of $\mathcal{F}$ means?

Published on 03 Apr 2026 - 21:28

score 83 · Answer 4 · 2026-04-04 02:44:45

83

Views

Prove Weierstrass theorem for a general $[a,b]$ follows from the result on $[0,1]$.

Published on 04 Apr 2026 - 2:44

score 480 · Answer 5 · 2026-04-05 04:02:16

480

Views

How to prove $f$ can be uniformly approximated on $[1,\infty )$ by a function $g$, using Weierstrass theorem.

Published on 05 Apr 2026 - 4:02

score 82 · Answer 6 · 2026-04-04 01:34:32

82

Views

Show $f$ is the uniform limit of $p_n\circ \cos,$ where the $p_n$ are polynomials.

Published on 04 Apr 2026 - 1:34

score 50 · Answer 7 · 2026-04-03 21:26:42

50

Views

Value of sum $\sum_{k=0}^{n}n_{C_k}\frac{k}{n}x^k(1-x)^{n-k}$ .

Published on 03 Apr 2026 - 21:26

score 156 · Answer 8 · 2026-04-04 05:20:39

156

Views

An application of Weierstrass Approximation Theorem to polynomial

Published on 04 Apr 2026 - 5:20

score 56 · Answer 9 · 2026-04-04 08:43:01

56

Views

For each $\epsilon>0$ there is a polynomial $p\colon\mathbb{C}\to\mathbb{C}$ such that $|p(x)-|x||<\epsilon$ for all $x\in[-r,r]$.

Published on 04 Apr 2026 - 8:43

score 833 · Answer 10 · 2026-04-04 13:43:03

833

Views

Does there exist a sequence of polynomials converging uniformly to $f(x) = |x| $ on $ℝ$?

Published on 04 Apr 2026 - 13:43

score 408 · Answer 11 · 2026-04-04 01:40:38

408

Views

Using weierstrass approximation theorem prove that polynomials are dense in $C(X,\Bbb{R})$.

Published on 04 Apr 2026 - 1:40

score 128 · Answer 12 · 2026-04-04 11:42:17

128

Views

Use of Stone-Weierstrass Theorem for $1/z$ on complex circle

Published on 04 Apr 2026 - 11:42

score 120 · Answer 13 · 2026-04-03 22:26:44

120

Views

Approximation of continuous functions vanishing at a point with polynomials vanishing at the same point

Published on 03 Apr 2026 - 22:26

score 95 · Answer 14 · 2026-04-04 05:08:40

Relationship between the composition of two real functions and their approximation polynomials (Weierstrass approximation theorem)

score 27 · Answer 15 · 2026-04-03 17:26:53

Relationship between the multiplication of two real functions and their approximation polynomials (Weierstrass approximation theorem)

List Question

If $p$ is a polynomial approximating a continuous function $h$, why can we assume $\left\|p\right\|_\infty\le\left\|h\right\|_\infty$?

Inequality of expectation in Weierstrass theorem

What does the phrase "by a polynomial in a finite number of functions of $\mathcal{F}$ means?

Prove Weierstrass theorem for a general $[a,b]$ follows from the result on $[0,1]$.

How to prove $f$ can be uniformly approximated on $[1,\infty )$ by a function $g$, using Weierstrass theorem.

Show $f$ is the uniform limit of $p_n\circ \cos,$ where the $p_n$ are polynomials.

Value of sum $\sum_{k=0}^{n}n_{C_k}\frac{k}{n}x^k(1-x)^{n-k}$ .

An application of Weierstrass Approximation Theorem to polynomial

For each $\epsilon>0$ there is a polynomial $p\colon\mathbb{C}\to\mathbb{C}$ such that $|p(x)-|x||<\epsilon$ for all $x\in[-r,r]$.

Does there exist a sequence of polynomials converging uniformly to $f(x) = |x| $ on $ℝ$?

Using weierstrass approximation theorem prove that polynomials are dense in $C(X,\Bbb{R})$.

Use of Stone-Weierstrass Theorem for $1/z$ on complex circle

Approximation of continuous functions vanishing at a point with polynomials vanishing at the same point

Relationship between the composition of two real functions and their approximation polynomials (Weierstrass approximation theorem)

Relationship between the multiplication of two real functions and their approximation polynomials (Weierstrass approximation theorem)

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