Question

Asymptotic behaviour of Fourier transform: $|F[f]|=|\lambda^{-k}F[f^{(k)}]|$ for absolutely continuous $f$

score 229 · Answer 1 · 2014-11-20 18:27:08

229

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Asymptotic behaviour of Fourier transform: $|F[f]|=|\lambda^{-k}F[f^{(k)}]|$ for absolutely continuous $f$

Published on 20 Nov 2014 - 18:27

score 54 · Answer 2 · 2026-04-08 23:00:09

54

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$\frac{\varphi(x+h)-\varphi(x)}{h}\to\varphi'(x)$ uniformly as $h\to 0$?

Published on 08 Apr 2026 - 23:00

score 71 · Answer 3 · 2014-11-20 20:17:35

71

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Suppose $f$ is integrable on $\mathbb{R}$, and $g$ is locally integrable and bounded. Then $f*g$ is uniformly continuous and bounded?

Published on 20 Nov 2014 - 20:17

score 1.1k · Answer 4 · 2026-04-02 07:20:37

1.1k

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Show that Fourier transformation is differentiable if $\int|xf(x)|\,d\lambda<\infty$

Published on 02 Apr 2026 - 7:20

score 1k · Answer 5 · 2026-03-27 10:16:44

1k

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Difference between the Rectangular "Window" Function and the Rectangle Function

Published on 27 Mar 2026 - 10:16

score 1.1k · Answer 6 · 2014-11-20 23:20:19

1.1k

Views

Laplace equation on infinite strip

Published on 20 Nov 2014 - 23:20

score 184 · Answer 7 · 2026-03-29 09:41:00

184

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If $X_1,X_2,X$ are iid random variables with $X_1+X_2$ has the distribution of $aX$, find all characteristic functions of $X$.

Published on 29 Mar 2026 - 9:41

score 1k · Answer 8 · 2026-03-30 20:52:59

1k

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the Fourier transform of a constant

Published on 30 Mar 2026 - 20:52

score 85 · Answer 9 · 2014-11-21 07:43:27

85

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Using Fourier analysis to show a function is positive

Published on 21 Nov 2014 - 7:43

score 9k · Answer 10 · 2026-04-02 07:23:05

9k

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Derivative of Fourier transform: $F[f]'=F[-ixf(x)]$

Published on 02 Apr 2026 - 7:23

score 1.1k · Answer 11 · 2014-11-21 16:23:15

1.1k

Views

Multidimensional Fourier Transform

Published on 21 Nov 2014 - 16:23

score 532 · Answer 12 · 2026-04-09 04:50:01

532

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Fourier transforms in combinatorics

Published on 09 Apr 2026 - 4:50

score 275 · Answer 13 · 2026-04-02 09:15:16

275

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$\int_{\mathbb{R}}f(x)e^{-ixz}d\mu_x$ analytic for $f\in L_1$

Published on 02 Apr 2026 - 9:15

score 2.4k · Answer 14 · 2026-03-26 01:34:55

2.4k

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Finding Fourier cosine series of sine function

Published on 26 Mar 2026 - 1:34

score 386 · Answer 15 · 2026-03-27 04:17:34

386

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$\{x^nf(x)\}_{n\in\mathbb{N}}\subset L_2(a,b)$ as a complete system

Published on 27 Mar 2026 - 4:17

List Question

Asymptotic behaviour of Fourier transform: $|F[f]|=|\lambda^{-k}F[f^{(k)}]|$ for absolutely continuous $f$

$\frac{\varphi(x+h)-\varphi(x)}{h}\to\varphi'(x)$ uniformly as $h\to 0$?

Suppose $f$ is integrable on $\mathbb{R}$, and $g$ is locally integrable and bounded. Then $f*g$ is uniformly continuous and bounded?

Show that Fourier transformation is differentiable if $\int|xf(x)|\,d\lambda<\infty$

Difference between the Rectangular "Window" Function and the Rectangle Function

Laplace equation on infinite strip

If $X_1,X_2,X$ are iid random variables with $X_1+X_2$ has the distribution of $aX$, find all characteristic functions of $X$.

the Fourier transform of a constant

Using Fourier analysis to show a function is positive

Derivative of Fourier transform: $F[f]'=F[-ixf(x)]$

Multidimensional Fourier Transform

Fourier transforms in combinatorics

$\int_{\mathbb{R}}f(x)e^{-ixz}d\mu_x$ analytic for $f\in L_1$

Finding Fourier cosine series of sine function

$\{x^nf(x)\}_{n\in\mathbb{N}}\subset L_2(a,b)$ as a complete system

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