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 39 · Answer 1 · 2020-12-09 08:19:18

39

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 09 Dec 2020 - 8:19

score 61 · Answer 2 · 2020-12-22 11:48:10

61

Views

Inequality of expectation in Weierstrass theorem

Published on 22 Dec 2020 - 11:48

score 84 · Answer 3 · 2021-01-02 23:27:02

84

Views

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

Published on 02 Jan 2021 - 23:27

score 80 · Answer 4 · 2021-01-21 00:43:29

80

Views

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

Published on 21 Jan 2021 - 0:43

score 477 · Answer 5 · 2021-01-23 06:52:24

477

Views

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

Published on 23 Jan 2021 - 6:52

score 80 · Answer 6 · 2021-01-25 23:25:17

80

Views

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

Published on 25 Jan 2021 - 23:25

score 47 · Answer 7 · 2021-01-26 14:10:49

47

Views

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

Published on 26 Jan 2021 - 14:10

score 153 · Answer 8 · 2021-02-11 05:48:30

153

Views

An application of Weierstrass Approximation Theorem to polynomial

Published on 11 Feb 2021 - 5:48

score 53 · Answer 9 · 2021-02-26 11:23:52

53

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 26 Feb 2021 - 11:23

score 830 · Answer 10 · 2021-03-11 20:18:40

830

Views

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

Published on 11 Mar 2021 - 20:18

score 405 · Answer 11 · 2021-04-08 19:03:12

405

Views

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

Published on 08 Apr 2021 - 19:03

score 125 · Answer 12 · 2021-05-26 10:35:21

125

Views

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

Published on 26 May 2021 - 10:35

score 117 · Answer 13 · 2021-06-11 04:32:02

117

Views

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

Published on 11 Jun 2021 - 4:32

score 92 · Answer 14 · 2021-06-18 21:05:29

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

score 24 · Answer 15 · 2021-06-19 19:30:24

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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