Question

Suppose $f\in L_2(\mathbb R)$ and $f$ is a continuous function on $\mathbb R$. Is $\displaystyle\sum_{k\in\mathbb{Z}}|f(k)|^2<\infty $?

score 99 · Answer 1 · 2026-03-29 20:51:34

99

Views

Suppose $f\in L_2(\mathbb R)$ and $f$ is a continuous function on $\mathbb R$. Is $\displaystyle\sum_{k\in\mathbb{Z}}|f(k)|^2<\infty $?

Published on 29 Mar 2026 - 20:51

score 1.2k · Answer 2 · 2026-03-26 07:35:40

1.2k

Views

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 3 · 2026-03-26 23:10:35

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 26 Mar 2026 - 23:10

score 288 · Answer 4 · 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 90 · Answer 5 · 2026-03-26 19:20:08

90

Views

Finding the expansion coefficients of the decomposition of a 3D Gaussian wavepacket in the eigenfunctions of the Hydrogen atom

Published on 26 Mar 2026 - 19:20

score 160 · Answer 6 · 2026-03-29 20:49:40

160

Views

How to derive Riesz transform from its Fourier transform?

Published on 29 Mar 2026 - 20:49

score 56 · Answer 7 · 2026-03-28 09:09:24

56

Views

A question bout Fourier coefficients

Published on 28 Mar 2026 - 9:09

score 117 · Answer 8 · 2026-03-28 03:16:10

117

Views

Is it possible to isolate and thereby by integration compute a zeta zero gap when accentuating the zeros and counting them?

Published on 28 Mar 2026 - 3:16

score 43 · Answer 9 · 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 1.2k · Answer 10 · 2026-03-25 12:52:26

1.2k

Views

A question about Bochner's theorem.

Published on 25 Mar 2026 - 12:52

score 870 · Answer 11 · 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

score 1k · Answer 12 · 2026-03-25 11:16:05

1k

Views

Expanding the function $f(x) = 1, 0 < x < 1$ in a series of the eigenfunctions?

Published on 25 Mar 2026 - 11:16

score 53 · Answer 13 · 2026-03-25 17:44:54

53

Views

Time-Averaged Fourier Transform

Published on 25 Mar 2026 - 17:44

score 37 · Answer 14 · 2026-03-27 01:46:43

37

Views

Regarding Fourier transform of $\int_{0}^{t}f(e^{i \tau})d\tau$

Published on 27 Mar 2026 - 1:46

score 79 · Answer 15 · 2026-03-27 05:03:28

79

Views

Calculate the integral $\int_{\frac{5\pi}{2}}^{\frac{9\pi}{2}} \cos^4{\theta}\;d\theta.$

Published on 27 Mar 2026 - 5:03

List Question

Suppose $f\in L_2(\mathbb R)$ and $f$ is a continuous function on $\mathbb R$. Is $\displaystyle\sum_{k\in\mathbb{Z}}|f(k)|^2<\infty $?

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: $f(x)=\begin{cases}x+1 & -1\leq x< 0,\\1-x &0\leq x< 1\end{cases},\;\;f(x+2)=f(x)$

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

Finding the expansion coefficients of the decomposition of a 3D Gaussian wavepacket in the eigenfunctions of the Hydrogen atom

How to derive Riesz transform from its Fourier transform?

A question bout Fourier coefficients

Is it possible to isolate and thereby by integration compute a zeta zero gap when accentuating the zeros and counting them?

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

A question about Bochner's theorem.

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

Expanding the function $f(x) = 1, 0 < x < 1$ in a series of the eigenfunctions?

Time-Averaged Fourier Transform

Regarding Fourier transform of $\int_{0}^{t}f(e^{i \tau})d\tau$

Calculate the integral $\int_{\frac{5\pi}{2}}^{\frac{9\pi}{2}} \cos^4{\theta}\;d\theta.$

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