Question

Why $\int_0^{2\pi} \sin^2 x \mathrm{d}x \neq \int_0^{2\pi}\sin x \sin nx \mathrm{d}x \to n=1$

score 71 · Answer 1 · 2026-03-26 22:16:10

71

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Why $\int_0^{2\pi} \sin^2 x \mathrm{d}x \neq \int_0^{2\pi}\sin x \sin nx \mathrm{d}x \to n=1$

Published on 26 Mar 2026 - 22:16

score 289 · Answer 2 · 2018-12-13 02:31:37

289

Views

Proof of Poisson Summation Formula

Published on 13 Dec 2018 - 2:31

score 52 · Answer 3 · 2018-12-13 17:00:47

52

Views

Finding a series of cosines to represent the absolute value function

Published on 13 Dec 2018 - 17:00

score 242 · Answer 4 · 2026-04-01 22:50:24

242

Views

Extra factor of 2 when evaluating an infinite sum using fourier series and parseval's theorem.

Published on 01 Apr 2026 - 22:50

score 71 · Answer 5 · 2026-03-25 06:20:20

71

Views

Understanding Y U Egorov's theorem

Published on 25 Mar 2026 - 6:20

score 85 · Answer 6 · 2018-12-14 19:17:17

85

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Solution of $u_t=\mathcal{F}u$

Published on 14 Dec 2018 - 19:17

score 538 · Answer 7 · 2026-03-25 14:21:30

538

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Example of a non-trace class operator

Published on 25 Mar 2026 - 14:21

score 294 · Answer 8 · 2026-03-26 00:58:41

294

Views

Applying sine orthogonality

Published on 26 Mar 2026 - 0:58

score 63 · Answer 9 · 2026-03-28 03:27:40

63

Views

$\lVert f \rVert _{H^{s}(\mathbb{R}^d )} \leq C \lVert f \rVert_{L^{1} (\mathbb{R}^d )}$ cannot hold at $ s= -d/2$.

Published on 28 Mar 2026 - 3:27

score 92 · Answer 10 · 2026-03-27 02:34:10

92

Views

Technical operator theory question on Albeverio's "Solvable Models in quantum mechanics"

Published on 27 Mar 2026 - 2:34

score 89 · Answer 11 · 2018-12-18 13:00:58

89

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Compute $\frac{1}{2\pi}\int_0^{2\pi}f(t)g(t)dt$ where $g(t)= \sum\limits_{n=1}^\infty \frac{(-1)^n}{n}\sin(nt)$

Published on 18 Dec 2018 - 13:00

score 1.5k · Answer 12 · 2026-03-28 05:22:37

1.5k

Views

Inverse Fourier transformation of $\frac{1}{(1+w^2)^2}$?

Published on 28 Mar 2026 - 5:22

score 175 · Answer 13 · 2026-03-27 11:49:10

175

Views

Is there a proof of the real form of Fourier's Theorem?

Published on 27 Mar 2026 - 11:49

score 2.8k · Answer 14 · 2026-03-28 07:57:07

2.8k

Views

L^2 convergence and pointwise convergence

Published on 28 Mar 2026 - 7:57

score 229 · Answer 15 · 2026-03-25 12:54:38

229

Views

Is there an analogue of the Fourier transform based on hyperbolic trig functions?

Published on 25 Mar 2026 - 12:54

List Question

Why $\int_0^{2\pi} \sin^2 x \mathrm{d}x \neq \int_0^{2\pi}\sin x \sin nx \mathrm{d}x \to n=1$

Proof of Poisson Summation Formula

Finding a series of cosines to represent the absolute value function

Extra factor of 2 when evaluating an infinite sum using fourier series and parseval's theorem.

Understanding Y U Egorov's theorem

Solution of $u_t=\mathcal{F}u$

Example of a non-trace class operator

Applying sine orthogonality

$\lVert f \rVert _{H^{s}(\mathbb{R}^d )} \leq C \lVert f \rVert_{L^{1} (\mathbb{R}^d )}$ cannot hold at $ s= -d/2$.

Technical operator theory question on Albeverio's "Solvable Models in quantum mechanics"

Compute $\frac{1}{2\pi}\int_0^{2\pi}f(t)g(t)dt$ where $g(t)= \sum\limits_{n=1}^\infty \frac{(-1)^n}{n}\sin(nt)$

Inverse Fourier transformation of $\frac{1}{(1+w^2)^2}$?

Is there a proof of the real form of Fourier's Theorem?

L^2 convergence and pointwise convergence

Is there an analogue of the Fourier transform based on hyperbolic trig functions?

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