List questions from harmonic-analysis

Published on 23 Jan 2018 - 14:23

34

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Inequality $||\theta_x||_{L^{\infty}}+||\mathcal{H}\theta_x||_{L^{\infty}}\leq C ||\theta||_{H^{2}}$

Published on 25 Mar 2026 - 3:04

67

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"Classical inequality" regarding the Bessel potential space $H^{-1}$

Published on 17 Mar 2026 - 14:50

276

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Justifying connection between convergence of Fourier transform and Fourier Series for $L^2$ function

Published on 25 Jan 2018 - 10:38

69

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Decomposition of the representation $\chi_m(t)=e^{imt}$?

Published on 25 Mar 2026 - 13:41

229

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How to show range of a projection is an eigenspace.

Published on 24 Mar 2026 - 20:58

100

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Show to which $A$ and $B$ the Fourier series converges uniformly

Published on 25 Mar 2026 - 6:06

111

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Restrict $g$ to a dense subclass in $\|f\|_p=\text{sup}\{|\int_Xfg|:\|g\|_{p'}\leq 1\}$

Published on 27 Mar 2026 - 12:23

50

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Show $\|f\|_p\leq\|f\|_q\mu(X)^{\frac{1}{p}-\frac{1}{q}}$ whenever $0<p\leq q\leq \infty$ using log-convexity of $L^p$ norms.

Published on 27 Jan 2018 - 12:09

128

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Bochner nonnegativity theorem for Laplace-Beltrami eigenfunctions?

Published on 19 Mar 2026 - 19:11

308

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Fourier transform on the special orthogonal group

Published on 24 Mar 2026 - 23:44

118

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Decomposition of $L^2(S^1)$

Published on 17 Mar 2026 - 9:37

262

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Different proof of the Plancherel Formula in $L^2(\mathbb R).$

Published on 24 Mar 2026 - 23:45

41

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How to prove $g(x,y) = \int_{0}^{2\pi} u(e^{i\theta}(x+iy)) sin(\theta)d\theta$ is a polynomial if $u$ is harmonic?

Published on 01 Feb 2018 - 21:22

700

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Bounding Fejer kernel

Published on 16 Mar 2026 - 21:01

List Question

Elementary proof of norm convergence of Inverse Fourier Transform for $L^2$ function

Inequality $||\theta_x||_{L^{\infty}}+||\mathcal{H}\theta_x||_{L^{\infty}}\leq C ||\theta||_{H^{2}}$

"Classical inequality" regarding the Bessel potential space $H^{-1}$

Justifying connection between convergence of Fourier transform and Fourier Series for $L^2$ function

Decomposition of the representation $\chi_m(t)=e^{imt}$?

How to show range of a projection is an eigenspace.

Show to which $A$ and $B$ the Fourier series converges uniformly

Restrict $g$ to a dense subclass in $\|f\|_p=\text{sup}\{|\int_Xfg|:\|g\|_{p'}\leq 1\}$

Show $\|f\|_p\leq\|f\|_q\mu(X)^{\frac{1}{p}-\frac{1}{q}}$ whenever $0<p\leq q\leq \infty$ using log-convexity of $L^p$ norms.

Bochner nonnegativity theorem for Laplace-Beltrami eigenfunctions?

Fourier transform on the special orthogonal group

Decomposition of $L^2(S^1)$

Different proof of the Plancherel Formula in $L^2(\mathbb R).$

How to prove $g(x,y) = \int_{0}^{2\pi} u(e^{i\theta}(x+iy)) sin(\theta)d\theta$ is a polynomial if $u$ is harmonic?

Bounding Fejer kernel

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