List questions from harmonic-analysis

Published on 07 Apr 2026 - 3:32

200

Views

Is $\sum_{k=2}^\infty \frac{\cos((2k^2-k+7)x)}{k(\ln k)^2}$ a Fourier series?

Published on 20 Apr 2017 - 0:37

100

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find a limit of a distribution

Published on 07 Apr 2026 - 3:35

553

Views

translation invariant distribution

Published on 07 Apr 2026 - 3:32

79

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fourier transform for $H_s$ function

Published on 07 Apr 2026 - 3:31

76

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Invertible harmonic oscillator

Published on 26 Mar 2026 - 16:03

340

Views

Littlewood-Paley decomposition in Tao's note

Published on 22 Apr 2017 - 8:23

136

Views

Confusion about the definition of Plancherel measure for finite groups

Published on 07 Apr 2026 - 19:47

153

Views

Show that $f \in H^{\frac{1}{2}}$, using that $\iint_{\mathbb{T}^1\times \mathbb{T}^1} \frac{|f(x)-f(y)|^2}{sin^2(\pi(x-y))} \,dx\,dy < \infty$

Published on 25 Apr 2017 - 16:52

187

Views

What does the Bourgain norm tell us about a function?

Published on 26 Apr 2017 - 2:58

599

Views

Bessel functions in resolution of second order ODE

Published on 02 Apr 2026 - 1:22

47

Views

If $f\in L^{2}(G)$ and $G$ is abelian, must $f(\cdot^{-1})\in L^{2}(G)$ also?

Published on 26 Apr 2017 - 19:54

994

Views

Approximation of continuous polynomials by trigonometric polynomials in proof of Fejér Sum Convergence

Published on 02 May 2017 - 18:41

208

Views

Proving the quantitative uncertainty principle

Published on 04 May 2017 - 20:58

82

Views

Is it true that for $f\in\mathscr{S}(\mathbb{R}^n)$, we have $\widehat{\lvert\nabla f\rvert}=\left\lvert\widehat{\nabla f}\right\rvert$?

Published on 05 May 2017 - 4:23

List Question

Prove it is a distribution

Is $\sum_{k=2}^\infty \frac{\cos((2k^2-k+7)x)}{k(\ln k)^2}$ a Fourier series?

find a limit of a distribution

translation invariant distribution

fourier transform for $H_s$ function

Invertible harmonic oscillator

Littlewood-Paley decomposition in Tao's note

Confusion about the definition of Plancherel measure for finite groups

Show that $f \in H^{\frac{1}{2}}$, using that $\iint_{\mathbb{T}^1\times \mathbb{T}^1} \frac{|f(x)-f(y)|^2}{sin^2(\pi(x-y))} \,dx\,dy < \infty$

What does the Bourgain norm tell us about a function?

Bessel functions in resolution of second order ODE

If $f\in L^{2}(G)$ and $G$ is abelian, must $f(\cdot^{-1})\in L^{2}(G)$ also?

Approximation of continuous polynomials by trigonometric polynomials in proof of Fejér Sum Convergence

Proving the quantitative uncertainty principle

Is it true that for $f\in\mathscr{S}(\mathbb{R}^n)$, we have $\widehat{\lvert\nabla f\rvert}=\left\lvert\widehat{\nabla f}\right\rvert$?

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