Question

If $f$ is Riemann-integrable, $\int_{-\pi}^{\pi}|\sigma_Nf(x)-f(x)|dx \rightarrow 0$ as $N\rightarrow\infty$

score 149 · Answer 1 · 2020-05-05 23:46:27

149

Views

If $f$ is Riemann-integrable, $\int_{-\pi}^{\pi}|\sigma_Nf(x)-f(x)|dx \rightarrow 0$ as $N\rightarrow\infty$

Published on 05 May 2020 - 23:46

score 937 · Answer 2 · 2020-05-11 16:43:07

937

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Show that the Fejér Kernel $F_n$ is a good kernel and $\int_{0}^{1}F_n(x)dx = 1$

Published on 11 May 2020 - 16:43

score 142 · Answer 3 · 2020-05-11 18:05:39

142

Views

Why does the Dirichlet Kernel $D_N$, the sum of exponentials gives $\frac{1}{2\pi}\int_{-\pi}^{\pi}D_N(x)~dx =1$?

Published on 11 May 2020 - 18:05

score 140 · Answer 4 · 2020-06-25 17:26:45

140

Views

Integrating powers of the Fejer kernel

Published on 25 Jun 2020 - 17:26

score 889 · Answer 5 · 2016-09-20 03:35:26

889

Views

Bounding Derivative of Fejer Kernel

Published on 20 Sep 2016 - 3:35

score 3.1k · Answer 6 · 2015-12-24 15:55:10

3.1k

Views

Properties of the Fejer kernel

Published on 24 Dec 2015 - 15:55

score 207 · Answer 7 · 2016-01-27 20:43:21

207

Views

Prove an equality involving Fejer Kernel

Published on 27 Jan 2016 - 20:43

score 1k · Answer 8 · 2017-08-04 06:40:07

1k

Views

How do I prove my Fejer kernel definition is equivalent?

Published on 04 Aug 2017 - 6:40

score 101 · Answer 9 · 2017-10-24 12:54:52

101

Views

Is there a closed form for the "positive summands" of the fejer kernel?

Published on 24 Oct 2017 - 12:54

score 819 · Answer 10 · 2017-11-21 11:15:17

819

Views

Fejer's theorem for Fourier transforms of $L^1(\mathbb{R})$ functions

Published on 21 Nov 2017 - 11:15

score 130 · Answer 11 · 2018-01-09 09:16:15

130

Views

Real analysis and convergence versus $\int_0^1\sum_{n=1}^\infty x^2\mu(n)\frac{1-\cos(nx)}{n(1-\cos(x))}dx$, where $\mu(n)$ is the Möbius function

Published on 09 Jan 2018 - 9:16

score 273 · Answer 12 · 2012-07-24 14:05:24

273

Views

Fejer kernel applied to a measure

Published on 24 Jul 2012 - 14:05

score 1.4k · Answer 13 · 2012-12-10 00:25:03

1.4k

Views

Property of Fejer kernel

Published on 10 Dec 2012 - 0:25

score 104 · Answer 14 · 2021-01-07 08:01:21

104

Views

summation methode of Fejér

Published on 07 Jan 2021 - 8:01

score 317 · Answer 15 · 2021-04-11 01:00:46

317

Views

Fourier coefficients of Cesaro means of partial fourier series

Published on 11 Apr 2021 - 1:00

List Question

If $f$ is Riemann-integrable, $\int_{-\pi}^{\pi}|\sigma_Nf(x)-f(x)|dx \rightarrow 0$ as $N\rightarrow\infty$

Show that the Fejér Kernel $F_n$ is a good kernel and $\int_{0}^{1}F_n(x)dx = 1$

Why does the Dirichlet Kernel $D_N$, the sum of exponentials gives $\frac{1}{2\pi}\int_{-\pi}^{\pi}D_N(x)~dx =1$?

Integrating powers of the Fejer kernel

Bounding Derivative of Fejer Kernel

Properties of the Fejer kernel

Prove an equality involving Fejer Kernel

How do I prove my Fejer kernel definition is equivalent?

Is there a closed form for the "positive summands" of the fejer kernel?

Fejer's theorem for Fourier transforms of $L^1(\mathbb{R})$ functions

Real analysis and convergence versus $\int_0^1\sum_{n=1}^\infty x^2\mu(n)\frac{1-\cos(nx)}{n(1-\cos(x))}dx$, where $\mu(n)$ is the Möbius function

Fejer kernel applied to a measure

Property of Fejer kernel

summation methode of Fejér

Fourier coefficients of Cesaro means of partial fourier series

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