List questions from weierstrass-approximation

Published on 23 Jun 2021 - 12:57

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Can polynomials with coefficients in [-1, 1] uniformly approximate arbitrarily large constant functions?

Published on 29 Jun 2021 - 11:14

158

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$\int_0^1 f(x)e^{nx} \, dx=0$ for all $n \in \Bbb N\cup{\{0\}}$ implies $f(x) = 0$

Published on 06 Jul 2021 - 2:28

73

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Determining the fractal dimension of the series $\sum_{n=1}^{\infty} \sin{(n^2x)^2/n^3}$

Published on 25 Jul 2021 - 15:26

158

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$C_0^\infty(\mathbb{R}^k)$ functions can be approximated via polynomials

Published on 04 Aug 2021 - 15:48

564

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Weierstrass approximation theorem in two dimensions

Published on 09 Aug 2021 - 13:40

380

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Baby Rudin Theorem 8.15: Approximate periodic continuous function by trigonometric polynomials

Published on 16 Aug 2021 - 6:58

105

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Approximating $\bar{z}$ on unit arc

Published on 25 Aug 2021 - 2:47

132

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Baby Rudin Theorem 7.33

Published on 30 Aug 2021 - 15:32

206

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Proof of Stone's generalization of Weierstrass theorem in PMA by Walter Rudin

Published on 18 Sep 2021 - 8:22

86

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A $T_{3\frac{1}{2}}$ space is compact if Stone-Weierstrass theorem holds.

Published on 05 Oct 2021 - 14:47

104

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Analytic Continuation of a function defined in integral

Published on 04 Nov 2021 - 9:46

229

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How to prove Algebra generated by$\{1,e^{ix}\}$ is dense in $C([0,\pi],\mathbb C)$?

Published on 14 Nov 2021 - 15:37

48

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Is this conclusion on stone-weierstrass approximation true?

Published on 15 Nov 2021 - 0:27

80

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What are the applications of the second part of the Stone-Weierstrass theorem?

Published on 07 Jan 2022 - 7:29

List Question

Proof — Weierstrass Approximation Theory for derivatives

Can polynomials with coefficients in [-1, 1] uniformly approximate arbitrarily large constant functions?

$\int_0^1 f(x)e^{nx} \, dx=0$ for all $n \in \Bbb N\cup{\{0\}}$ implies $f(x) = 0$

Determining the fractal dimension of the series $\sum_{n=1}^{\infty} \sin{(n^2x)^2/n^3}$

$C_0^\infty(\mathbb{R}^k)$ functions can be approximated via polynomials

Weierstrass approximation theorem in two dimensions

Baby Rudin Theorem 8.15: Approximate periodic continuous function by trigonometric polynomials

Approximating $\bar{z}$ on unit arc

Baby Rudin Theorem 7.33

Proof of Stone's generalization of Weierstrass theorem in PMA by Walter Rudin

A $T_{3\frac{1}{2}}$ space is compact if Stone-Weierstrass theorem holds.

Analytic Continuation of a function defined in integral

How to prove Algebra generated by$\{1,e^{ix}\}$ is dense in $C([0,\pi],\mathbb C)$?

Is this conclusion on stone-weierstrass approximation true?

What are the applications of the second part of the Stone-Weierstrass theorem?

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