List questions from harmonic-analysis

Published on 11 May 2026 - 4:36

128

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Show that if $f\in L^1(\mathbb{R})$ and $g\in S(\mathbb{R})$. then $f*g\in C(\mathbb{R})$

Published on 11 May 2026 - 1:53

94

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Give an example to show that not all smooth rapidly decreasing functions are Schwartz fiunctions.

Published on 11 May 2026 - 0:47

792

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Find the complex Fourier series of the $2\pi$ periodic function $f(x)=x^2$ and determine the function which the Fourier series converges to.

Published on 14 Apr 2026 - 3:53

62

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Find the exact number of times $f(x)=\displaystyle\sum_{n\neq 0}\frac{1}{n^{4.01}}e^{inx}$ is continuously differentiable.

Published on 15 Apr 2026 - 10:05

1.7k

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Haar measure on orthogonal group

Published on 11 Apr 2026 - 15:02

44

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Sovling classical parabolic equation by using Littlewood-Paley theory

Published on 09 Apr 2026 - 7:07

61

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For $f\in L^{\infty}(\mathbb R^n\ltimes SO(n))$ I do not understand this equality?

Published on 11 May 2026 - 0:53

213

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Divergence theorem for fractional Laplacian operator

Published on 09 Apr 2026 - 4:01

7.6k

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Why do we use trig functions in Fourier transforms, and not other periodic functions?

Published on 10 May 2026 - 14:31

80

Views

How to bound oscillatory integral?

Published on 08 Apr 2026 - 22:11

128

Views

Showing $|x|^\alpha$ is an $A_p$ weight for $-d<\alpha<d(p-1)$

Published on 16 Apr 2026 - 13:50

209

Views

Understanding kernel of Riesz transforms $K(r,\zeta)=r^{-2}\Omega(\zeta)$

Published on 09 Apr 2026 - 3:20

77

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Closedness of Bessel vector space

Published on 16 Apr 2026 - 1:31

312

Views

Inequality of p-norm for Hardy-Littlewood maximum function

Published on 10 May 2026 - 17:12

List Question

Bound on trigonometric polynomials in terms of derivative

Show that if $f\in L^1(\mathbb{R})$ and $g\in S(\mathbb{R})$. then $f*g\in C(\mathbb{R})$

Give an example to show that not all smooth rapidly decreasing functions are Schwartz fiunctions.

Find the complex Fourier series of the $2\pi$ periodic function $f(x)=x^2$ and determine the function which the Fourier series converges to.

Find the exact number of times $f(x)=\displaystyle\sum_{n\neq 0}\frac{1}{n^{4.01}}e^{inx}$ is continuously differentiable.

Haar measure on orthogonal group

Sovling classical parabolic equation by using Littlewood-Paley theory

For $f\in L^{\infty}(\mathbb R^n\ltimes SO(n))$ I do not understand this equality?

Divergence theorem for fractional Laplacian operator

Why do we use trig functions in Fourier transforms, and not other periodic functions?

How to bound oscillatory integral?

Showing $|x|^\alpha$ is an $A_p$ weight for $-d<\alpha<d(p-1)$

Understanding kernel of Riesz transforms $K(r,\zeta)=r^{-2}\Omega(\zeta)$

Closedness of Bessel vector space

Inequality of p-norm for Hardy-Littlewood maximum function

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