Question

What is the difference between Fourier coefficients and Fourier transforms in this context?

score 53 · Answer 1 · 2026-04-09 17:09:23

53

Views

What is the difference between Fourier coefficients and Fourier transforms in this context?

Published on 09 Apr 2026 - 17:09

score 35 · Answer 2 · 2026-04-15 11:00:39

35

Views

If $\phi \in L^1(\mathbb{R})$ is sufficiently nice, then $\exists f \in L^1(\mathbb{R})$ such that its Fourier transform is $\phi$

Published on 15 Apr 2026 - 11:00

score 337 · Answer 3 · 2026-04-09 20:13:33

337

Views

How to obtain solution to constants "c_n" from Fourier's trick?

Published on 09 Apr 2026 - 20:13

score 171 · Answer 4 · 2026-04-15 12:30:26

171

Views

Fourier series for $f(t)=\cos(t)$.

Published on 15 Apr 2026 - 12:30

score 922 · Answer 5 · 2026-04-12 03:00:29

922

Views

Why, traditionally, does FFT use complex numbers as a wrapper for magnitude and phase?

Published on 12 Apr 2026 - 3:00

score 905 · Answer 6 · 2026-04-11 02:29:59

905

Views

Proof of relation between smoothness of a function and rapid decay of its Fourier coefficients

Published on 11 Apr 2026 - 2:29

score 34 · Answer 7 · 2026-04-15 03:22:27

34

Views

For which $p>0$ is the series L^2-convergent?

Published on 15 Apr 2026 - 3:22

score 138 · Answer 8 · 2026-04-10 17:12:47

138

Views

Checking the validity of Green function using a operator using a certain limit

Published on 10 Apr 2026 - 17:12

score 708 · Answer 9 · 2026-04-18 15:28:04

708

Views

Equidistribution of $\big(\frac{1+ \sqrt{5}}{2}\big)^n$ in $[0,1]$

Published on 18 Apr 2026 - 15:28

score 675 · Answer 10 · 2026-04-09 17:33:45

675

Views

Prove that the Fourier transform of a test function has not compact support

Published on 09 Apr 2026 - 17:33

score 249 · Answer 11 · 2026-04-11 14:07:39

249

Views

Compact Support of Fourier-like Differential Form $\sigma(\xi)$

Published on 11 Apr 2026 - 14:07

score 79 · Answer 12 · 2026-04-16 17:42:54

79

Views

Why is $\int_{-\infty}^{\infty}e^{itx}\frac{1}{\pi(1+x^2)}dx=\sqrt{\frac{2}{\pi}}\int_0^{\infty}e^{-\frac{1}{2}\left(y^2+ \frac{t^2}{y^2}\right)}dy$?

Published on 16 Apr 2026 - 17:42

score 54 · Answer 13 · 2026-04-17 19:05:32

54

Views

Error in "proof" that $l^1$ and $l^2$-summability of $\hat{f}$ implies $L^4$-integrability of $f$

Published on 17 Apr 2026 - 19:05

score 479 · Answer 14 · 2026-04-16 02:43:23

479

Views

Prove that $\int_0^\pi f^2\leq \int_0^\pi (f')^2$ by Wirtinger's inequality

Published on 16 Apr 2026 - 2:43

score 342 · Answer 15 · 2026-04-11 08:00:37

342

Views

What assumptions are needed for the convolution theorems to hold?

Published on 11 Apr 2026 - 8:00

List Question

What is the difference between Fourier coefficients and Fourier transforms in this context?

If $\phi \in L^1(\mathbb{R})$ is sufficiently nice, then $\exists f \in L^1(\mathbb{R})$ such that its Fourier transform is $\phi$

How to obtain solution to constants "c_n" from Fourier's trick?

Fourier series for $f(t)=\cos(t)$.

Why, traditionally, does FFT use complex numbers as a wrapper for magnitude and phase?

Proof of relation between smoothness of a function and rapid decay of its Fourier coefficients

For which $p>0$ is the series L^2-convergent?

Checking the validity of Green function using a operator using a certain limit

Equidistribution of $\big(\frac{1+ \sqrt{5}}{2}\big)^n$ in $[0,1]$

Prove that the Fourier transform of a test function has not compact support

Compact Support of Fourier-like Differential Form $\sigma(\xi)$

Why is $\int_{-\infty}^{\infty}e^{itx}\frac{1}{\pi(1+x^2)}dx=\sqrt{\frac{2}{\pi}}\int_0^{\infty}e^{-\frac{1}{2}\left(y^2+ \frac{t^2}{y^2}\right)}dy$?

Error in "proof" that $l^1$ and $l^2$-summability of $\hat{f}$ implies $L^4$-integrability of $f$

Prove that $\int_0^\pi f^2\leq \int_0^\pi (f')^2$ by Wirtinger's inequality

What assumptions are needed for the convolution theorems to hold?

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