Question

Can every real continuous function be approximated by either a convex or concave function on an interval?

score 114 · Answer 1 · 2023-09-17 11:35:04

114

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Can every real continuous function be approximated by either a convex or concave function on an interval?

Published on 17 Sep 2023 - 11:35

score 34 · Answer 2 · 2023-10-10 08:43:21

34

Views

Lower bound function with simpler function

Published on 10 Oct 2023 - 8:43

score 93 · Answer 3 · 2023-11-20 02:58:43

93

Views

Are polynomials dense in $C^1([0, 1]^n)$?

Published on 20 Nov 2023 - 2:58

score 81 · Answer 4 · 2023-12-05 13:19:13

81

Views

proof of Stone–Weierstrass Theorem

Published on 05 Dec 2023 - 13:19

score 54 · Answer 5 · 2023-12-29 08:41:10

54

Views

How to prove that an absolutely continuous function space on a finite closed interval is a separable space in this norm sense?

Published on 29 Dec 2023 - 8:41

score 67 · Answer 6 · 2024-01-09 17:52:43

67

Views

Topological field without the Stone-Weierstrass property

Published on 09 Jan 2024 - 17:52

score 28 · Answer 7 · 2024-03-21 00:58:59

28

Views

Explicit approximation of $C_0(\mathbf{N})$ using elementary functions

Published on 21 Mar 2024 - 0:58

score 2.5k · Answer 8 · 2016-03-11 22:32:20

2.5k

Views

Uniform approximation by even polynomial

Published on 11 Mar 2016 - 22:32

score 111 · Answer 9 · 2016-03-15 18:49:03

111

Views

Using Weierstrass to prove certain limit: Carothers Ch.11 q.10

Published on 15 Mar 2016 - 18:49

score 165 · Answer 10 · 2016-05-03 23:59:02

165

Views

Describe the intervals where $f_n(x)$ converges uniformly

Published on 03 May 2016 - 23:59

score 2.1k · Answer 11 · 2016-05-22 05:15:15

2.1k

Views

$\bar{z}$ cannot be uniformly approximated by polynomials in $z$ on the closed unit disc in $\mathbb{C}$.

Published on 22 May 2016 - 5:15

score 438 · Answer 12 · 2016-06-27 11:32:59

438

Views

Showing a 2D continuous function can be approximated by a finite sum of "simpler" continuous functions

Published on 27 Jun 2016 - 11:32

score 823 · Answer 13 · 2017-04-25 16:26:23

823

Views

Proof explanation of Stone-Weierstrass theorem

Published on 25 Apr 2017 - 16:26

score 719 · Answer 14 · 2017-04-25 18:48:10

719

Views

Explanation of Stone-Weierstrass theorem's proof

Published on 25 Apr 2017 - 18:48

score 63 · Answer 15 · 2017-05-10 10:45:22

63

Views

$X:=\{z \in \mathbb C : |z|\le 1\}$ ; is $\{p(z,\bar z) | p(x,y) \in \mathbb R[x,y] \}$ dense in $C(X , \mathbb C) $ under sup metric?

Published on 10 May 2017 - 10:45

List Question

Can every real continuous function be approximated by either a convex or concave function on an interval?

Lower bound function with simpler function

Are polynomials dense in $C^1([0, 1]^n)$?

proof of Stone–Weierstrass Theorem

How to prove that an absolutely continuous function space on a finite closed interval is a separable space in this norm sense?

Topological field without the Stone-Weierstrass property

Explicit approximation of $C_0(\mathbf{N})$ using elementary functions

Uniform approximation by even polynomial

Using Weierstrass to prove certain limit: Carothers Ch.11 q.10

Describe the intervals where $f_n(x)$ converges uniformly

$\bar{z}$ cannot be uniformly approximated by polynomials in $z$ on the closed unit disc in $\mathbb{C}$.

Showing a 2D continuous function can be approximated by a finite sum of "simpler" continuous functions

Proof explanation of Stone-Weierstrass theorem

Explanation of Stone-Weierstrass theorem's proof

$X:=\{z \in \mathbb C : |z|\le 1\}$ ; is $\{p(z,\bar z) | p(x,y) \in \mathbb R[x,y] \}$ dense in $C(X , \mathbb C) $ under sup metric?

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