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Problem about Weierstrass Approximation

score 975 · Answer 1 · 2016-12-14 16:52:11

975

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Problem about Weierstrass Approximation

Published on 14 Dec 2016 - 16:52

score 177 · Answer 2 · 2016-12-18 19:07:14

177

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

Published on 18 Dec 2016 - 19:07

score 692 · Answer 3 · 2016-12-23 11:53:49

692

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The Series of functions in Weierstrass M test

Published on 23 Dec 2016 - 11:53

score 847 · Answer 4 · 2017-01-03 00:16:20

847

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

Published on 03 Jan 2017 - 0:16

score 259 · Answer 5 · 2017-01-29 23:16:22

259

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

Published on 29 Jan 2017 - 23:16

score 799 · Answer 6 · 2017-02-21 11:48:20

799

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A density proof not via Stone-Weierstrass

Published on 21 Feb 2017 - 11:48

score 1k · Answer 7 · 2017-02-26 02:42:59

1k

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Weierstrass approximation theorem - absolute value

Published on 26 Feb 2017 - 2:42

score 1.3k · Answer 8 · 2017-03-01 09:38:10

1.3k

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Help proving the Weierstrass Approximation Theorem using Fejer's Theorem

Published on 01 Mar 2017 - 9:38

score 308 · Answer 9 · 2017-03-13 19:11:51

308

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

Published on 13 Mar 2017 - 19:11

score 2.7k · Answer 10 · 2017-03-24 02:49:25

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 24 Mar 2017 - 2:49

score 979 · Answer 11 · 2023-01-31 00:35:31

979

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Proof of Weierstrass approximation theorem

Published on 31 Jan 2023 - 0:35

score 64 · Answer 12 · 2023-02-04 12:08:46

64

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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 04 Feb 2023 - 12:08

score 68 · Answer 13 · 2023-02-24 23:49:59

68

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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 24 Feb 2023 - 23:49

score 55 · Answer 14 · 2023-03-12 21:23:17

55

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

Published on 12 Mar 2023 - 21:23

score 93 · Answer 15 · 2023-03-20 18:43:10

93

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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 20 Mar 2023 - 18:43

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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