Question

Is the identity $(\chi_V,\chi_V)=\sum_{i=1}^k a_i^2$ appearing in character theory related to Parseval’s identity from Fourier analysis?

score 38 · Answer 1 · 2026-04-12 02:59:21

38

Views

Is the identity $(\chi_V,\chi_V)=\sum_{i=1}^k a_i^2$ appearing in character theory related to Parseval’s identity from Fourier analysis?

Published on 12 Apr 2026 - 2:59

score 34 · Answer 2 · 2026-04-16 13:36:05

34

Views

$\lim_{n\to\infty}\int_0^1 f(x,\sin nt)dt=\frac{1}{2\pi}\int_0^{2\pi}f(x,\sin y)d y$ for continuous $f$

Published on 16 Apr 2026 - 13:36

score 117 · Answer 3 · 2026-04-13 18:03:45

117

Views

Does the Fourier series of abs(x) converge uniformly?

Published on 13 Apr 2026 - 18:03

score 62 · Answer 4 · 2026-04-17 14:36:38

Prove that $ I = \int_{0}^1 \sin(2 \pi x) e^{-2 \pi ikx} dx = \begin{cases} \frac{-ki}{2}, & \text{if $k=\pm1$ } \\ 0, & \text{if $k=0$} \end{cases}$

score 109 · Answer 5 · 2026-04-14 01:07:36

109

Views

$\pi / 4 \not = \sum_{n, \text { odd }}^{\infty} \frac{1}{n} \sin \left(n \pi \frac{z}{h}\right)$ but the author argues otherwise

Published on 14 Apr 2026 - 1:07

score 53 · Answer 6 · 2026-04-16 13:12:28

53

Views

Calculate the Fourier series of $f(x)= \frac{1}{2} - |x-\frac{1}{2}| $

Published on 16 Apr 2026 - 13:12

score 32 · Answer 7 · 2026-04-12 15:42:13

32

Views

The sum of the series(in functional series)

Published on 12 Apr 2026 - 15:42

score 20 · Answer 8 · 2026-04-29 15:25:32

20

Views

Extreme sensitivity to the input scale of a Continuous Fourier Transform approximation from Discrete Fourier Transform

Published on 29 Apr 2026 - 15:25

score 63 · Answer 9 · 2026-04-11 02:58:35

63

Views

Fourier series converges absolutely almost everywhere to smooth function. Maybe also everywhere?

Published on 11 Apr 2026 - 2:58

score 620 · Answer 10 · 2026-04-16 07:01:07

620

Views

$\sum_{k=1}^\infty\frac{1}{k^4} = \frac{\pi^4}{90}$ using Parseval's Theorem and Fourier series

Published on 16 Apr 2026 - 7:01

score 59 · Answer 11 · 2026-04-15 08:05:11

59

Views

What's special about cosine and polynomial?

Published on 15 Apr 2026 - 8:05

score 118 · Answer 12 · 2026-04-12 05:59:39

118

Views

Transform Fourier of paths in symplectic vector spaces

Published on 12 Apr 2026 - 5:59

score 271 · Answer 13 · 2026-04-12 00:15:44

271

Views

Mistake in proof of Lemma 2.3 in Chapter 3 of Stein and Shakarchi's Fourier Analysis

Published on 12 Apr 2026 - 0:15

score 96 · Answer 14 · 2026-04-09 18:47:00

96

Views

Fourier series of $\cos(\pi w x)$

Published on 09 Apr 2026 - 18:47

score 34 · Answer 15 · 2026-04-17 02:44:29

34

Views

Does an entire periodic function has an everywhere convergent Fourier series?

Published on 17 Apr 2026 - 2:44

List Question

Is the identity $(\chi_V,\chi_V)=\sum_{i=1}^k a_i^2$ appearing in character theory related to Parseval’s identity from Fourier analysis?

$\lim_{n\to\infty}\int_0^1 f(x,\sin nt)dt=\frac{1}{2\pi}\int_0^{2\pi}f(x,\sin y)d y$ for continuous $f$

Does the Fourier series of abs(x) converge uniformly?

Prove that $ I = \int_{0}^1 \sin(2 \pi x) e^{-2 \pi ikx} dx = \begin{cases} \frac{-ki}{2}, & \text{if $k=\pm1$ } \\ 0, & \text{if $k=0$} \end{cases}$

$\pi / 4 \not = \sum_{n, \text { odd }}^{\infty} \frac{1}{n} \sin \left(n \pi \frac{z}{h}\right)$ but the author argues otherwise

Calculate the Fourier series of $f(x)= \frac{1}{2} - |x-\frac{1}{2}| $

The sum of the series(in functional series)

Extreme sensitivity to the input scale of a Continuous Fourier Transform approximation from Discrete Fourier Transform

Fourier series converges absolutely almost everywhere to smooth function. Maybe also everywhere?

$\sum_{k=1}^\infty\frac{1}{k^4} = \frac{\pi^4}{90}$ using Parseval's Theorem and Fourier series

What's special about cosine and polynomial?

Transform Fourier of paths in symplectic vector spaces

Mistake in proof of Lemma 2.3 in Chapter 3 of Stein and Shakarchi's Fourier Analysis

Fourier series of $\cos(\pi w x)$

Does an entire periodic function has an everywhere convergent Fourier series?

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