Questions tagged [harmonic-analysis]

Question 1

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 ...

Question 2

I want to prove that $C^{*}(G)\cong \oplus_{\pi\in\hat{G}}M_{dim\pi}(\mathbb{C})$. Of course, one wants to use the Peter-Weyl theorem for this (the version, which states that $L^{2}(G)\cong \oplus_{\...

Question 3

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 ...

Question 4

I’m trying to understand a step in Appendix A.1 of Bejenaru and Herr, The cubic Dirac equation: small initial data in $H^1(\mathbb{R}^3)$. The paper proves global well-posedness for the cubic Dirac ...

Question 5

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 ...

Question 6

What is the Haar measure on the Bohr compactification $b\mathbb{Z}$ of the integers? We (my collaborators and I) suspect that it is $$ \int_{b\mathbb{Z}} d\mu_H f(n) = \lim_{N\to\infty}\frac{1}{2N+1} \...

Question 7

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 ...

Question 8

I want to show that $C^{*}(G)\cong C_{0}(\hat{G})$, where G is a locally compact abelian group. I alredy know that, since G is abelian $C^{*}(G)$ is also abelian and that one applies the Gelfand ...

Question 9

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 ...

Question 10

I'm currently studying interpolation spaces, but I'm struggling to understand some of the intuition behind real interpolation. There are two equivalent methods to define the real interpolation functor,...

Question 11

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 $...

Question 12

Suppose that there is a group action on a manifold, $G\times M\to M$. Does the space of functions on $M$ decompose into the direct sum of irreducible representations of $G$? I am familiar with the (...

Question 13

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 ...

Question 14

I am currently trying to solve the heat equation on the integers (viewed as an LCA group) using the Fourier transform on the integers. Of course one can't take the normal Laplace operator, but instead ...

Question 15

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 ...

Stack Exchange Network

Questions tagged [harmonic-analysis]

Fourier inversion theorem for compact groups

Classification of $C^{*}(G)$ for a compact group $G$

On the convolution identity of a sub arc of circle and the open set which is thickened epsilon amount of another subarc in circle.

Can Young's inequality give a pointwise bound for a convolution?

Why is the Reciprocal Log Transform so "un-creative"? Why does it seem to "interpolate" between Fourier, Mellin and Laplace?

What is the Haar measure on the Bohr compactification $b\mathbb{Z}$ of the integers?

What do self-adjoint operators on $L^2(\mathbb{A}_{\mathbb{Q}}^{\times} / \mathbb{Q}^{\times})$ look like?

Classification of an LCA group C*-algebra

Understanding an argument involving integration by parts and an estimate for the gradient

Real interpolation: Why do the J- and K-methods scale everything by 1/t?

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 there exist a decompositions for the space of functions on manifolds with group action?

Reference request: tensor products of principal series of $SL(2,\mathbb{C})$

Solving the Heat equation on the integers via Fourier transformation

Help in understanding a localization argument for norm inequalities

Hot Network Questions