Question

Parseval identity $\int_0^1|f(x)|^2dx=\sum\limits_{n\in\mathbf Z}|\hat f_n|^2$ weaker condition

score 115 · Answer 1 · 2026-04-14 17:02:00

115

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Parseval identity $\int_0^1|f(x)|^2dx=\sum\limits_{n\in\mathbf Z}|\hat f_n|^2$ weaker condition

Published on 14 Apr 2026 - 17:02

score 43 · Answer 2 · 2026-04-16 02:17:19

43

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Showing $\int_0^1f\bar g =\sum\limits_{n\in\mathbf Z}\hat f_n\overline{\hat g_n}$

Published on 16 Apr 2026 - 2:17

score 61 · Answer 3 · 2026-04-09 01:14:34

61

Views

Finding Area to integrate

Published on 09 Apr 2026 - 1:14

score 180 · Answer 4 · 2026-04-12 01:40:47

180

Views

Three questions on Fourier Transforms

Published on 12 Apr 2026 - 1:40

score 262 · Answer 5 · 2026-04-14 05:53:47

262

Views

Why the range of time period of exponential Fourier series is different from other two types of Fourier series?

Published on 14 Apr 2026 - 5:53

score 340 · Answer 6 · 2026-03-27 03:45:25

340

Views

Intuition for polynomial bases

Published on 27 Mar 2026 - 3:45

score 133 · Answer 7 · 2026-04-14 19:38:17

133

Views

Fourier basis of $L^2([-\pi,\pi])$

Published on 14 Apr 2026 - 19:38

score 10.7k · Answer 8 · 2026-04-08 16:34:39

10.7k

Views

Fourier Series of $\cos(ax)$

Published on 08 Apr 2026 - 16:34

score 50 · Answer 9 · 2026-04-10 13:17:51

50

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Fourier series of a complicated function

Published on 10 Apr 2026 - 13:17

score 82 · Answer 10 · 2026-04-16 18:59:43

82

Views

Series expansion of {x}

Published on 16 Apr 2026 - 18:59

score 96 · Answer 11 · 2026-04-14 02:18:22

96

Views

The indefinite integral of an $L^1$ function has a convergent series of Fourier coefficients

Published on 14 Apr 2026 - 2:18

score 216 · Answer 12 · 2026-04-13 06:02:44

216

Views

Example of fourier series diverges at least two points

Published on 13 Apr 2026 - 6:02

score 39 · Answer 13 · 2026-03-29 03:36:26

39

Views

Writing an operator $T$ defined by $(T f)(t) = \int_{-\pi}^\pi h(t − s)f(s)ds$ as $\sum_{n \in \mathbb Z} \mu_n \langle f, \varphi_n\rangle \varphi_n$

Published on 29 Mar 2026 - 3:36

score 4.2k · Answer 14 · 2026-04-15 09:15:11

4.2k

Views

Find the Fourier series of $x^2$ over $[-\pi,\pi]$

Published on 15 Apr 2026 - 9:15

score 2.2k · Answer 15 · 2026-04-10 21:21:09

2.2k

Views

How to justify interchange of sum and integral in fourier series?

Published on 10 Apr 2026 - 21:21

List Question

Parseval identity $\int_0^1|f(x)|^2dx=\sum\limits_{n\in\mathbf Z}|\hat f_n|^2$ weaker condition

Showing $\int_0^1f\bar g =\sum\limits_{n\in\mathbf Z}\hat f_n\overline{\hat g_n}$

Finding Area to integrate

Three questions on Fourier Transforms

Why the range of time period of exponential Fourier series is different from other two types of Fourier series?

Intuition for polynomial bases

Fourier basis of $L^2([-\pi,\pi])$

Fourier Series of $\cos(ax)$

Fourier series of a complicated function

Series expansion of {x}

The indefinite integral of an $L^1$ function has a convergent series of Fourier coefficients

Example of fourier series diverges at least two points

Writing an operator $T$ defined by $(T f)(t) = \int_{-\pi}^\pi h(t − s)f(s)ds$ as $\sum_{n \in \mathbb Z} \mu_n \langle f, \varphi_n\rangle \varphi_n$

Find the Fourier series of $x^2$ over $[-\pi,\pi]$

How to justify interchange of sum and integral in fourier series?

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