Question

Is the set of all polynomials dense in the set of all continuous functions that maps from a compact set to reals

score 725 · Answer 1 · 2017-12-07 17:15:32

725

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Is the set of all polynomials dense in the set of all continuous functions that maps from a compact set to reals

Published on 07 Dec 2017 - 17:15

score 32 · Answer 2 · 2017-12-09 13:11:53

32

Views

How to show $B_n(f)^2\le B_n(f^2)$

Published on 09 Dec 2017 - 13:11

score 357 · Answer 3 · 2017-12-09 19:12:00

357

Views

polynomials converging point wise to $f$ on $\mathbb{R}$

Published on 09 Dec 2017 - 19:12

score 1.1k · Answer 4 · 2017-12-26 22:59:55

1.1k

Views

Stone-Weierstrass complex theorem

Published on 26 Dec 2017 - 22:59

score 227 · Answer 5 · 2020-08-04 07:04:52

227

Views

Prove any smooth function with compact support can be uniformly approximated by elements in the space generated by $f_a(x)=e^{iax}e^{-x^2}$.

Published on 04 Aug 2020 - 7:04

score 37 · Answer 6 · 2020-08-18 20:34:42

37

Views

A statement of double integral which is closely related to Weierstrass approximation theorem

Published on 18 Aug 2020 - 20:34

score 248 · Answer 7 · 2020-09-22 07:09:38

248

Views

$f\in C [-1,1]$ and $\int_{-1}^1 f(x) x^{2n} dx=0$ implies $f$ is odd function?

Published on 22 Sep 2020 - 7:09

score 25 · Answer 8 · 2020-09-28 07:00:31

25

Views

Equivalent statement of Weierstrass approximation theorem.

Published on 28 Sep 2020 - 7:00

score 89 · Answer 9 · 2020-10-14 16:26:37

89

Views

Weierstrass Approximation generalization

Published on 14 Oct 2020 - 16:26

score 113 · Answer 10 · 2020-10-30 07:01:26

113

Views

A related question to the Weierstrass approximation theorem

Published on 30 Oct 2020 - 7:01

score 59 · Answer 11 · 2020-11-19 00:05:48

59

Views

$\int_0^1 f(t)e^{nt} dt = 0 \implies f \equiv 0 $ an application of Stone-Weierstrass

Published on 19 Nov 2020 - 0:05

score 342 · Answer 12 · 2020-11-20 11:52:31

342

Views

$ \int_a^bx^nf(x)\mathrm{d}x=0,\ n=0,1,2,\cdots. $ Prove that $f=0$.

Published on 20 Nov 2020 - 11:52

score 104 · Answer 13 · 2020-11-21 12:30:33

104

Views

Riemann-integral and Stone-Weierstrauss Theorem

Published on 21 Nov 2020 - 12:30

score 624 · Answer 14 · 2020-11-26 14:30:43

624

Views

Using Stone-Weierstrass theorem prove that $f\equiv 0$ in $[0,1]$ under certain conditions.

Published on 26 Nov 2020 - 14:30

score 143 · Answer 15 · 2020-12-02 04:53:12

143

Views

Rate of approximation by polynomials to a C1 function(Weierstras Approximation thm)

Published on 02 Dec 2020 - 4:53

List Question

Is the set of all polynomials dense in the set of all continuous functions that maps from a compact set to reals

How to show $B_n(f)^2\le B_n(f^2)$

polynomials converging point wise to $f$ on $\mathbb{R}$

Stone-Weierstrass complex theorem

Prove any smooth function with compact support can be uniformly approximated by elements in the space generated by $f_a(x)=e^{iax}e^{-x^2}$.

A statement of double integral which is closely related to Weierstrass approximation theorem

$f\in C [-1,1]$ and $\int_{-1}^1 f(x) x^{2n} dx=0$ implies $f$ is odd function?

Equivalent statement of Weierstrass approximation theorem.

Weierstrass Approximation generalization

A related question to the Weierstrass approximation theorem

$\int_0^1 f(t)e^{nt} dt = 0 \implies f \equiv 0 $ an application of Stone-Weierstrass

$ \int_a^bx^nf(x)\mathrm{d}x=0,\ n=0,1,2,\cdots. $ Prove that $f=0$.

Riemann-integral and Stone-Weierstrauss Theorem

Using Stone-Weierstrass theorem prove that $f\equiv 0$ in $[0,1]$ under certain conditions.

Rate of approximation by polynomials to a C1 function(Weierstras Approximation thm)

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