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Very basic question : A sequence $\{a_n\}\in \ell^2$ determines a function $f\in L^2[-\pi,\pi]$ with Fourier coefficients $a_n$

score 27 · Answer 1 · 2023-06-09 05:10:58

27

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Very basic question : A sequence $\{a_n\}\in \ell^2$ determines a function $f\in L^2[-\pi,\pi]$ with Fourier coefficients $a_n$

Published on 09 Jun 2023 - 5:10

score 108 · Answer 2 · 2026-04-01 15:45:31

108

Views

Fourier Series of product of two functions with different period

Published on 01 Apr 2026 - 15:45

score 166 · Answer 3 · 2023-06-09 17:24:29

166

Views

Fourier transform $f(x)=\sin(x/2)$ in $0 \leq x < 2\pi$

Published on 09 Jun 2023 - 17:24

score 58 · Answer 4 · 2026-03-28 00:50:54

58

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Show Fourier series can be rearranged to equal a series

Published on 28 Mar 2026 - 0:50

score 30 · Answer 5 · 2026-03-28 22:28:27

30

Views

Fourier series of $\sin (n\rho) \,\frac{1-e^{(\lambda -\zeta n^2)t}}{\zeta n^2-\lambda}$

Published on 28 Mar 2026 - 22:28

score 44 · Answer 6 · 2023-06-12 19:45:45

44

Views

integral of series multiplied by function rules

Published on 12 Jun 2023 - 19:45

score 60 · Answer 7 · 2023-06-13 07:30:38

60

Views

Can the series be the Fourier series?

Published on 13 Jun 2023 - 7:30

score 168 · Answer 8 · 2026-03-25 07:48:37

168

Views

Inverse function of $U_{k-1}(\cos(\frac{\pi}{x}))$?

Published on 25 Mar 2026 - 7:48

score 353 · Answer 9 · 2026-03-26 04:14:08

353

Views

a functional inequality (positive functions on circle)

Published on 26 Mar 2026 - 4:14

score 62 · Answer 10 · 2026-04-07 22:02:33

62

Views

Extending the calculation of fourier coefficients to general interval

Published on 07 Apr 2026 - 22:02

score 59 · Answer 11 · 2026-03-26 06:27:26

59

Views

Fourier Transform of random mapping

Published on 26 Mar 2026 - 6:27

score 76 · Answer 12 · 2023-06-16 21:15:33

76

Views

Solution of the heat equation and Fourier series

Published on 16 Jun 2023 - 21:15

score 261 · Answer 13 · 2026-02-23 15:11:13

261

Views

Does this Fourier Legendre series inverting $\frac65\frac{x^x}{x+1}-\frac35$ diverge or it is a software issue past $\approx 25$ series terms?

Published on 23 Feb 2026 - 15:11

score 81 · Answer 14 · 2023-06-17 22:36:21

81

Views

Fourier series for $\cos(x)^n$

Published on 17 Jun 2023 - 22:36

score 48 · Answer 15 · 2026-03-30 00:19:22

48

Views

Laurent expansion for $f(1/z)$, with $f$ an integer function.

Published on 30 Mar 2026 - 0:19

List Question

Very basic question : A sequence $\{a_n\}\in \ell^2$ determines a function $f\in L^2[-\pi,\pi]$ with Fourier coefficients $a_n$

Fourier Series of product of two functions with different period

Fourier transform $f(x)=\sin(x/2)$ in $0 \leq x < 2\pi$

Show Fourier series can be rearranged to equal a series

Fourier series of $\sin (n\rho) \,\frac{1-e^{(\lambda -\zeta n^2)t}}{\zeta n^2-\lambda}$

integral of series multiplied by function rules

Can the series be the Fourier series?

Inverse function of $U_{k-1}(\cos(\frac{\pi}{x}))$?

a functional inequality (positive functions on circle)

Extending the calculation of fourier coefficients to general interval

Fourier Transform of random mapping

Solution of the heat equation and Fourier series

Does this Fourier Legendre series inverting $\frac65\frac{x^x}{x+1}-\frac35$ diverge or it is a software issue past $\approx 25$ series terms?

Fourier series for $\cos(x)^n$

Laurent expansion for $f(1/z)$, with $f$ an integer function.

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