Question

Weak convergence implies strong convergence in $L^1$ for Fourier series?

score 1.5k · Answer 1 · 2026-03-20 12:08:50

Weak convergence implies strong convergence in $L^1$ for Fourier series?

Published on 20 Mar 2026 - 12:08

score 198 · Answer 2 · 2018-08-14 18:14:57

If $f\in L^1(\mathbb{T})$ is such that $\forall n<0, \hat{f}(n)=0$, does the Fourier series of $f$ converges in $L^1(\mathbb{T})$ norm to $f$?

score 259 · Answer 3 · 2026-03-22 11:37:57

259

Views

Constant term of weakly modular form of weight 2 vanishes

Published on 22 Mar 2026 - 11:37

score 316 · Answer 4 · 2018-08-15 18:34:16

316

Views

The $L^1$ convergence of Fourier series without absolute value

Published on 15 Aug 2018 - 18:34

score 102 · Answer 5 · 2018-08-16 01:20:06

102

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Similar uses of Taylor Series and Fourier Series

Published on 16 Aug 2018 - 1:20

score 137 · Answer 6 · 2018-08-17 23:10:43

137

Views

Coefficients in Generalised Fourier series Given By $c_k = \langle f, \psi_k \rangle$? $c_k$ Implicitly Chosen So That Sum Converges?

Published on 17 Aug 2018 - 23:10

score 1.2k · Answer 7 · 2026-03-26 07:35:40

1.2k

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Fourier Sine series uses the orthogonal set $\{\sin(nx)\}^\infty_{n = 1}$ on $0 \le x \le \pi$

Published on 26 Mar 2026 - 7:35

score 3.2k · Answer 8 · 2018-08-19 15:08:31

3.2k

Views

Find the Fourier series of the function: $f(x)=\begin{cases}x+1 & -1\leq x< 0,\\1-x &0\leq x< 1\end{cases},\;\;f(x+2)=f(x)$

Published on 19 Aug 2018 - 15:08

score 127 · Answer 9 · 2018-08-19 16:05:20

127

Views

Complex Fourier series of $ f=|2t|$ in domain $[-1,1]$

Published on 19 Aug 2018 - 16:05

score 288 · Answer 10 · 2026-03-26 07:35:29

288

Views

How Does a Fourier $\sin$/$\cos$ Series Arise From a "Normal" Fourier Series? How Does This Relate to the Generalised Fourier Series?

Published on 26 Mar 2026 - 7:35

score 92 · Answer 11 · 2026-03-22 03:26:07

92

Views

Help with Fourier Series $\sum_{j=1}^{\infty} \frac{1}{j^{2k}}\sin{2\pi j x}$

Published on 22 Mar 2026 - 3:26

score 55 · Answer 12 · 2026-03-22 07:14:23

55

Views

A question bout Fourier coefficients

Published on 22 Mar 2026 - 7:14

score 43 · Answer 13 · 2026-03-26 07:35:21

43

Views

How Do I Go About Finding the Terms of the Fourier Series of Some $f(x)$ with Respect to an Orthogonal Set?

Published on 26 Mar 2026 - 7:35

score 1.3k · Answer 14 · 2026-03-25 11:04:48

1.3k

Views

Confusion for the solution of the heat equation in a one dimensional bar

Published on 25 Mar 2026 - 11:04

score 870 · Answer 15 · 2026-03-26 07:35:22

870

Views

Finding the Fourier-Bessel Series For $f(x) = x$, $0 < x < 2$, With Respect to the Orthogonal Set $\{ J_1 (k_n(x)) \}$

Published on 26 Mar 2026 - 7:35

List Question

Weak convergence implies strong convergence in $L^1$ for Fourier series?

If $f\in L^1(\mathbb{T})$ is such that $\forall n<0, \hat{f}(n)=0$, does the Fourier series of $f$ converges in $L^1(\mathbb{T})$ norm to $f$?

Constant term of weakly modular form of weight 2 vanishes

The $L^1$ convergence of Fourier series without absolute value

Similar uses of Taylor Series and Fourier Series

Coefficients in Generalised Fourier series Given By $c_k = \langle f, \psi_k \rangle$? $c_k$ Implicitly Chosen So That Sum Converges?

Fourier Sine series uses the orthogonal set $\{\sin(nx)\}^\infty_{n = 1}$ on $0 \le x \le \pi$

Find the Fourier series of the function: $f(x)=\begin{cases}x+1 & -1\leq x< 0,\\1-x &0\leq x< 1\end{cases},\;\;f(x+2)=f(x)$

Complex Fourier series of $ f=|2t|$ in domain $[-1,1]$

How Does a Fourier $\sin$/$\cos$ Series Arise From a "Normal" Fourier Series? How Does This Relate to the Generalised Fourier Series?

Help with Fourier Series $\sum_{j=1}^{\infty} \frac{1}{j^{2k}}\sin{2\pi j x}$

A question bout Fourier coefficients

How Do I Go About Finding the Terms of the Fourier Series of Some $f(x)$ with Respect to an Orthogonal Set?

Confusion for the solution of the heat equation in a one dimensional bar

Finding the Fourier-Bessel Series For $f(x) = x$, $0 < x < 2$, With Respect to the Orthogonal Set $\{ J_1 (k_n(x)) \}$

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