Question

Can you use the weierstrass approximation theorem to show the convergence of fourier series to its function?

score 18 · Answer 1 · 2023-03-24 09:52:37

18

Views

Can you use the weierstrass approximation theorem to show the convergence of fourier series to its function?

Published on 24 Mar 2023 - 9:52

score 90 · Answer 2 · 2023-03-30 08:19:56

90

Views

Does there exist a sequence of polynomials, interpolating a continuous function $f$ at a finite set of points converging uniformly to $f$?

Published on 30 Mar 2023 - 8:19

score 274 · Answer 3 · 2023-04-01 22:48:29

274

Views

Show that $X_n \rightarrow X$ converge in distribution if and only if $E(X^k_n) \rightarrow E(X^k)$ for all $k=0,1,2,...$

Published on 01 Apr 2023 - 22:48

score 84 · Answer 4 · 2023-05-02 18:44:51

84

Views

Characterisation of functions with an essential singularity

Published on 02 May 2023 - 18:44

score 156 · Answer 5 · 2023-05-04 08:07:04

156

Views

Application of weierstrass approximation to prove $f(x)=0$

Published on 04 May 2023 - 8:07

score 34 · Answer 6 · 2023-05-17 22:33:36

34

Views

$\big|P_n(x) - |x|\big| < 1/n$ for all $x \in [0,1]$ implies $\|P_n(f) - |f|\|_\infty < 1/n$

Published on 17 May 2023 - 22:33

score 21 · Answer 7 · 2023-05-22 16:20:56

21

Views

Function approximation based on "implicit function"

Published on 22 May 2023 - 16:20

score 60 · Answer 8 · 2023-06-10 02:45:47

60

Views

Polynomial approximation of continuous function on $[0,\infty)$

Published on 10 Jun 2023 - 2:45

score 42 · Answer 9 · 2023-06-13 09:10:29

42

Views

Korovkin's theorem exact convergence on $x \to 1, x \to x, x \to x^2$

Published on 13 Jun 2023 - 9:10

score 58 · Answer 10 · 2023-06-20 06:51:37

58

Views

Unclear passage (Weierstrass' Poly Approximation Theorem)

Published on 20 Jun 2023 - 6:51

score 66 · Answer 11 · 2023-06-20 17:00:48

66

Views

Weierstrass Approximation for functions and (jacobian) derivatives simultaneously

Published on 20 Jun 2023 - 17:00

score 19 · Answer 12 · 2023-07-12 17:11:51

19

Views

Approximation of differentiable functions

Published on 12 Jul 2023 - 17:11

score 50 · Answer 13 · 2023-08-31 17:39:55

50

Views

Showing measurable function is zero a.e.

Published on 31 Aug 2023 - 17:39

score 39 · Answer 14 · 2023-09-10 05:20:44

39

Views

Equivalence with the Weierstrass transform

Published on 10 Sep 2023 - 5:20

score 57 · Answer 15 · 2023-09-10 23:38:41

57

Views

How does one come up with this construction of approximating polynomials of $|x|$?

Published on 10 Sep 2023 - 23:38

List Question

Can you use the weierstrass approximation theorem to show the convergence of fourier series to its function?

Does there exist a sequence of polynomials, interpolating a continuous function $f$ at a finite set of points converging uniformly to $f$?

Show that $X_n \rightarrow X$ converge in distribution if and only if $E(X^k_n) \rightarrow E(X^k)$ for all $k=0,1,2,...$

Characterisation of functions with an essential singularity

Application of weierstrass approximation to prove $f(x)=0$

$\big|P_n(x) - |x|\big| < 1/n$ for all $x \in [0,1]$ implies $\|P_n(f) - |f|\|_\infty < 1/n$

Function approximation based on "implicit function"

Polynomial approximation of continuous function on $[0,\infty)$

Korovkin's theorem exact convergence on $x \to 1, x \to x, x \to x^2$

Unclear passage (Weierstrass' Poly Approximation Theorem)

Weierstrass Approximation for functions and (jacobian) derivatives simultaneously

Approximation of differentiable functions

Showing measurable function is zero a.e.

Equivalence with the Weierstrass transform

How does one come up with this construction of approximating polynomials of $|x|$?

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