Questions tagged [harmonic-analysis]
Harmonic analysis is the generalisation of Fourier analysis. Use this tag for analysis on locally compact groups (e.g. Pontryagin duality), eigenvalues of the Laplacian on compact manifolds or graphs, and the abstract study of Fourier transform on Euclidean spaces (singular integrals, Littlewood-Paley theory, etc). Use the (wavelets) tag for questions on wavelets, and the (fourier-analysis) for more elementary topics in Fourier theory.
2,985 questions
1 vote
0 answers
41 views
Fourier inversion theorem for compact groups
I am searching for a good reference for finding the fourier inversion theorem for compact (abelian, or non abelian) groups (we shall denote such a group by $G$). In particular, I would like to see a ...
- 53
0 votes
0 answers
24 views
On the convolution identity of a sub arc of circle and the open set which is thickened epsilon amount of another subarc in circle.
Let $\sigma_I=\{e^{2i\pi t}:t\in I\}$ and $\sigma_J=\{e^{2\pi i t}:t\in J\}$ be two disjoint subarcs on the the first quadrant of unit circle of arc length $\theta$, where $I,J\subseteq [0,1/4]$ of ...
2 votes
2 answers
171 views
Why is the Reciprocal Log Transform so "un-creative"? Why does it seem to "interpolate" between Fourier, Mellin and Laplace?
I'm struggling to provide a proper conceptual reason for what is going on here. For background, I was taught in school the three major transforms, Laplace first, Fourier second and Mellin last (but ...
- 1,199
3 votes
0 answers
50 views
What do self-adjoint operators on $L^2(\mathbb{A}_{\mathbb{Q}}^{\times} / \mathbb{Q}^{\times})$ look like?
Consider the Hilbert space $\mathcal{H}$ = $L^2(\mathbb{A}_{\mathbb{Q}}^{\times} / \mathbb{Q}^{\times})$, where $\mathbb{A}_{\mathbb{Q}}^{\times}$ is the idèle group of $\mathbb{Q}$ equipped with its ...
- 71
2 votes
0 answers
52 views
Understanding an argument involving integration by parts and an estimate for the gradient
This question is about a seemingly trivial argument in the paper "Maximal estimates for averages over space curves". For days now, I have been thinking to myself that I could write the proof ...
- 4,187
1 vote
1 answer
111 views
Is the space $AP(\mathbb{R})$ of Bohr's almost-periodic functions dense in $L_2(b\mathbb{R})$ ($b\mathbb{R}$ is the Bohr compactification)
Is the space $AP(\mathbb{R})$ of Bohr's almost-periodic functions dense in $L_2(b\mathbb{R},d\mu_H)$, where $b\mathbb{R}$ is the Bohr compactification of the reals and $d\mu_H$ is the Haar measure on $...
- 95
2 votes
0 answers
76 views
Reference request: tensor products of principal series of $SL(2,\mathbb{C})$
I am looking for a reference (a textbook, research paper, or lecture notes) that helps me find the rules for which finite-dimensional representations can appear in operator space of tensor product of ...
1 vote
1 answer
44 views
Help in understanding a localization argument for norm inequalities
I was reading the paper "Maximal estimates for averages over space curves" by Hyerim Ko, Sanghyuk Lee and Sewook Oh. In one of their proofs, the authors mention that to obtain a global norm ...
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