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Problem about Weierstrass Approximation

score 978 · Answer 1 · 2026-03-21 21:30:48

978

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Problem about Weierstrass Approximation

Published on 21 Mar 2026 - 21:30

score 180 · Answer 2 · 2026-03-22 11:45:49

180

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Show that there exist a sequence of function $g_n$ that converge uniformly to $f$

Published on 22 Mar 2026 - 11:45

score 695 · Answer 3 · 2026-03-22 07:23:44

695

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The Series of functions in Weierstrass M test

Published on 22 Mar 2026 - 7:23

score 850 · Answer 4 · 2026-03-22 06:13:53

850

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Polynomial approximation (Weierstrass' Theorem) with equality at the endpoints

Published on 22 Mar 2026 - 6:13

score 262 · Answer 5 · 2026-03-21 23:46:21

262

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Could you please help give a hint to solve this problem in real analysis (uniform convergence)?

Published on 21 Mar 2026 - 23:46

score 802 · Answer 6 · 2026-03-22 02:49:37

802

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A density proof not via Stone-Weierstrass

Published on 22 Mar 2026 - 2:49

score 1k · Answer 7 · 2026-03-21 21:40:47

1k

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Weierstrass approximation theorem - absolute value

Published on 21 Mar 2026 - 21:40

score 1.3k · Answer 8 · 2026-03-22 04:20:42

1.3k

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Help proving the Weierstrass Approximation Theorem using Fejer's Theorem

Published on 22 Mar 2026 - 4:20

score 311 · Answer 9 · 2026-03-22 08:08:20

311

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$h$ is strictly monotone iff polynomials in $h$ are uniformly dense

Published on 22 Mar 2026 - 8:08

score 2.7k · Answer 10 · 2026-03-22 04:38:05

2.7k

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Prove that there exists a sequence of polynomials $(p_n)$ that converges uniformly to $f$ on $[a,b]$

Published on 22 Mar 2026 - 4:38

score 980 · Answer 11 · 2026-02-23 06:35:38

980

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Proof of Weierstrass approximation theorem

Published on 23 Feb 2026 - 6:35

score 65 · Answer 12 · 2026-02-23 06:40:49

65

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Let $f \in \mathcal C_0$ and $\varepsilon >0$. Is there an explicit construction of $g\in\mathcal C_c^\infty$ such that $\|f-g\|_\infty <\varepsilon$?

Published on 23 Feb 2026 - 6:40

score 69 · Answer 13 · 2026-02-23 06:41:04

69

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Justify the interchange of limits for $\displaystyle\lim_{n \to \infty} \lim_{m \to \infty} (n+1) \int_0^1 x^nP_m(x)dx$ where $P_m(x)$ is a polynomial

Published on 23 Feb 2026 - 6:41

score 56 · Answer 14 · 2026-02-23 06:40:32

56

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Showing that the limit of an infinite product equals a sine function times a t term

Published on 23 Feb 2026 - 6:40

score 94 · Answer 15 · 2026-02-23 06:41:00

94

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Minimizing $\frac{1-\int_{1-\int_{0}^1 F(r)dr }^1 F(t) dt }{1-\int_{0}^1 F(t)^2 dt}$ for increasing function subject to $F(0)=0, F(1)=1$

Published on 23 Feb 2026 - 6:41

List Question

Problem about Weierstrass Approximation

Show that there exist a sequence of function $g_n$ that converge uniformly to $f$

The Series of functions in Weierstrass M test

Polynomial approximation (Weierstrass' Theorem) with equality at the endpoints

Could you please help give a hint to solve this problem in real analysis (uniform convergence)?

A density proof not via Stone-Weierstrass

Weierstrass approximation theorem - absolute value

Help proving the Weierstrass Approximation Theorem using Fejer's Theorem

$h$ is strictly monotone iff polynomials in $h$ are uniformly dense

Prove that there exists a sequence of polynomials $(p_n)$ that converges uniformly to $f$ on $[a,b]$

Proof of Weierstrass approximation theorem

Let $f \in \mathcal C_0$ and $\varepsilon >0$. Is there an explicit construction of $g\in\mathcal C_c^\infty$ such that $\|f-g\|_\infty <\varepsilon$?

Justify the interchange of limits for $\displaystyle\lim_{n \to \infty} \lim_{m \to \infty} (n+1) \int_0^1 x^nP_m(x)dx$ where $P_m(x)$ is a polynomial

Showing that the limit of an infinite product equals a sine function times a t term

Minimizing $\frac{1-\int_{1-\int_{0}^1 F(r)dr }^1 F(t) dt }{1-\int_{0}^1 F(t)^2 dt}$ for increasing function subject to $F(0)=0, F(1)=1$

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