Question

Does $\int_0^\infty f(x+\theta)g(x) \, dx=0 \ , \ \forall \theta \in \mathbb{R}$ imply $f=0$ almost everywhere if $g$ is smooth and strictly positive?

score 91 · Answer 1 · 2018-04-24 19:03:45

91

Views

Does $\int_0^\infty f(x+\theta)g(x) \, dx=0 \ , \ \forall \theta \in \mathbb{R}$ imply $f=0$ almost everywhere if $g$ is smooth and strictly positive?

Published on 24 Apr 2018 - 19:03

score 80 · Answer 2 · 2018-04-24 21:16:27

80

Views

Fourier transform of $g(x) = (1-|x|)1_{[-1,1]}$, Poisson sommation

Published on 24 Apr 2018 - 21:16

score 48 · Answer 3 · 2026-03-25 17:23:37

48

Views

Fourier Series on Mathematica

Published on 25 Mar 2026 - 17:23

score 791 · Answer 4 · 2018-04-25 01:22:09

791

Views

Proving the amount of zeroes for a trigonometric polynomial.

Published on 25 Apr 2018 - 1:22

score 1.2k · Answer 5 · 2018-04-25 14:25:27

1.2k

Views

Evaluate the integral $\int_{-\infty}^{\infty} e^{-x^2} e^{ix} dx$

Published on 25 Apr 2018 - 14:25

score 386 · Answer 6 · 2018-04-25 14:40:06

386

Views

How can $\sin(n \pi x)$ be a complete ONB of $L^2([0,1])$ when $-\Delta$ is positive on them

Published on 25 Apr 2018 - 14:40

score 119 · Answer 7 · 2018-04-25 15:08:06

119

Views

Integration using Theory of Fourier Transform

Published on 25 Apr 2018 - 15:08

score 203 · Answer 8 · 2018-04-25 16:37:55

203

Views

Fourier Transform of $v(x)=\frac{e^{ix}}{1+9x^2}$

Published on 25 Apr 2018 - 16:37

score 171 · Answer 9 · 2026-03-26 03:11:37

171

Views

Determine whether Certain Series is Fourier Series of Some Integrable Function

Published on 26 Mar 2026 - 3:11

score 94 · Answer 10 · 2026-03-26 04:53:31

Given any countable subset $A$ of $[-\pi, \pi]$, there exists a function $f \in C[-\pi, \pi]$ whose Fourier series diverges for all $x$ $\in$ $A$.

score 263 · Answer 11 · 2026-03-27 07:22:25

263

Views

What is the relation between 2d Fourier Transform and Plane Waves?

Published on 27 Mar 2026 - 7:22

score 91 · Answer 12 · 2018-04-25 19:50:54

91

Views

Fourier transform of $G_s(x) = \frac{1}{\sqrt{s}} e^{-\frac{\pi x^2}{s}}$

Published on 25 Apr 2018 - 19:50

score 88 · Answer 13 · 2026-03-27 07:43:16

88

Views

Limiting Behavior of the oscillating series

Published on 27 Mar 2026 - 7:43

score 1.6k · Answer 14 · 2018-04-26 12:36:16

1.6k

Views

Conditions for a nonnegative Fourier transform

Published on 26 Apr 2018 - 12:36

score 75 · Answer 15 · 2018-04-26 13:11:23

75

Views

Fourier transform, deduce $\frac{a}{\pi} \int_{\mathbb{R}} \frac{\cos(2\pi xt)}{a^2+t^2} dt = e^{-2\pi a|x|}$

Published on 26 Apr 2018 - 13:11

List Question

Does $\int_0^\infty f(x+\theta)g(x) \, dx=0 \ , \ \forall \theta \in \mathbb{R}$ imply $f=0$ almost everywhere if $g$ is smooth and strictly positive?

Fourier transform of $g(x) = (1-|x|)1_{[-1,1]}$, Poisson sommation

Fourier Series on Mathematica

Proving the amount of zeroes for a trigonometric polynomial.

Evaluate the integral $\int_{-\infty}^{\infty} e^{-x^2} e^{ix} dx$

How can $\sin(n \pi x)$ be a complete ONB of $L^2([0,1])$ when $-\Delta$ is positive on them

Integration using Theory of Fourier Transform

Fourier Transform of $v(x)=\frac{e^{ix}}{1+9x^2}$

Determine whether Certain Series is Fourier Series of Some Integrable Function

Given any countable subset $A$ of $[-\pi, \pi]$, there exists a function $f \in C[-\pi, \pi]$ whose Fourier series diverges for all $x$ $\in$ $A$.

What is the relation between 2d Fourier Transform and Plane Waves?

Fourier transform of $G_s(x) = \frac{1}{\sqrt{s}} e^{-\frac{\pi x^2}{s}}$

Limiting Behavior of the oscillating series

Conditions for a nonnegative Fourier transform

Fourier transform, deduce $\frac{a}{\pi} \int_{\mathbb{R}} \frac{\cos(2\pi xt)}{a^2+t^2} dt = e^{-2\pi a|x|}$

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