Question

Changing the length of an interval for the Fourier coefficients

score 3k · Answer 1 · 2026-03-21 17:48:10

3k

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Changing the length of an interval for the Fourier coefficients

Published on 21 Mar 2026 - 17:48

score 150 · Answer 2 · 2026-03-25 02:57:46

150

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Fourier Series-Distribution

Published on 25 Mar 2026 - 2:57

score 433 · Answer 3 · 2018-04-01 02:29:52

433

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Bound on trigonometric polynomials in terms of derivative

Published on 01 Apr 2018 - 2:29

score 257 · Answer 4 · 2018-04-01 18:51:57

257

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Doubt regarding Fourier series coefficients.

Published on 01 Apr 2018 - 18:51

score 134 · Answer 5 · 2018-04-02 07:09:34

134

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Verifying proof for $\int_{0}^{T}|f(x)|^{2}dx\le\frac{T^{2}}{4\pi^{2}}\int_{0}^{T}|f'(x)|^{2}dx$

Published on 02 Apr 2018 - 7:09

score 126 · Answer 6 · 2026-03-25 14:25:31

126

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Show that if $f\in L^1(\mathbb{R})$ and $g\in S(\mathbb{R})$. then $f*g\in C(\mathbb{R})$

Published on 25 Mar 2026 - 14:25

score 36 · Answer 7 · 2018-04-03 21:16:28

36

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Prove that $\lim_{N \to \infty} \left( \int_{\pi-\pi/(N+1/2)}^{\pi} \frac{\sin((N+1/2)t)}{\sin(t/2)} dt \right)= 0$

Published on 03 Apr 2018 - 21:16

score 77 · Answer 8 · 2018-04-04 03:38:19

77

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Show that $\bigg|\int_{0}^{T}\overline {f(t)}g(t)~dt\bigg|^{2}\le\frac{T^{2}}{4\pi^{2}}\int_{0}^{T}|f(t)|^{2}dt\int_{0}^{T}|g'(t)|^{2}dt$

Published on 04 Apr 2018 - 3:38

score 74 · Answer 9 · 2026-03-25 12:21:14

74

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The metric on L2 space expressed in terms of Fourier sine coefficients

Published on 25 Mar 2026 - 12:21

score 490 · Answer 10 · 2018-04-05 01:39:55

490

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Find Fourier Series of $f(x)=e^x+e^{-x}$

Published on 05 Apr 2018 - 1:39

score 2.3k · Answer 11 · 2018-04-05 05:30:01

2.3k

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Find Fourier Series of the function $f(x)=\sin x + \cos x$

Published on 05 Apr 2018 - 5:30

score 659 · Answer 12 · 2026-03-25 13:48:40

659

Views

On the asymptotic behavior of the Fourier coefficients of $(1-R\cos\theta)^{-3/2}$

Published on 25 Mar 2026 - 13:48

score 1.7k · Answer 13 · 2018-04-05 18:22:42

1.7k

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How to prove that the span of $\cos((n+1/2)x)$ and $\sin(nx)$ is dense in $L^2(-\pi,\pi)$?

Published on 05 Apr 2018 - 18:22

score 385 · Answer 14 · 2018-04-06 09:45:17

385

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Application of l'Hopital Rule to a Fourier Series

Published on 06 Apr 2018 - 9:45

score 457 · Answer 15 · 2026-03-25 03:19:44

457

Views

"Least Squares" of Dirac Delta?

Published on 25 Mar 2026 - 3:19

List Question

Changing the length of an interval for the Fourier coefficients

Fourier Series-Distribution

Bound on trigonometric polynomials in terms of derivative

Doubt regarding Fourier series coefficients.

Verifying proof for $\int_{0}^{T}|f(x)|^{2}dx\le\frac{T^{2}}{4\pi^{2}}\int_{0}^{T}|f'(x)|^{2}dx$

Show that if $f\in L^1(\mathbb{R})$ and $g\in S(\mathbb{R})$. then $f*g\in C(\mathbb{R})$

Prove that $\lim_{N \to \infty} \left( \int_{\pi-\pi/(N+1/2)}^{\pi} \frac{\sin((N+1/2)t)}{\sin(t/2)} dt \right)= 0$

Show that $\bigg|\int_{0}^{T}\overline {f(t)}g(t)~dt\bigg|^{2}\le\frac{T^{2}}{4\pi^{2}}\int_{0}^{T}|f(t)|^{2}dt\int_{0}^{T}|g'(t)|^{2}dt$

The metric on L2 space expressed in terms of Fourier sine coefficients

Find Fourier Series of $f(x)=e^x+e^{-x}$

Find Fourier Series of the function $f(x)=\sin x + \cos x$

On the asymptotic behavior of the Fourier coefficients of $(1-R\cos\theta)^{-3/2}$

How to prove that the span of $\cos((n+1/2)x)$ and $\sin(nx)$ is dense in $L^2(-\pi,\pi)$?

Application of l'Hopital Rule to a Fourier Series

"Least Squares" of Dirac Delta?

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