List questions from harmonic-analysis

Published on 06 May 2026 - 3:47

37

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

Published on 10 May 2026 - 12:34

70

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

Published on 11 Apr 2026 - 23:30

281

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

Published on 17 Apr 2026 - 14:19

75

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

Published on 13 May 2026 - 9:12

237

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How to show range of a projection is an eigenspace.

Published on 02 May 2026 - 18:20

109

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

Published on 10 May 2026 - 12:17

116

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

Published on 29 Apr 2026 - 12:24

53

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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 17 Apr 2026 - 8:14

136

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Bochner nonnegativity theorem for Laplace-Beltrami eigenfunctions?

Published on 07 May 2026 - 20:13

311

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Fourier transform on the special orthogonal group

Published on 10 May 2026 - 13:24

125

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

Published on 10 May 2026 - 18:39

265

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

Published on 10 May 2026 - 14:31

44

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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 15 Apr 2026 - 11:05

704

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Bounding Fejer kernel

Published on 12 Apr 2026 - 20:06

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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