# Tagged Questions

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-...

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### Do conformal maps preserve subsolutions of elliptic PDE?

The fact is well-known for the Laplace equation for regions in $\mathbb R^n$ but I'm wondering if it extends to general elliptic PDE.
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### Intuition regarding $\lim \lVert u_r - u \rVert_{p}=0$

I have some trouble intrepreting the following statment If $u$ is harmonic in $D$ and has bouned means for order p on circles of radius $< 1$ then $\lVert u \rVert_{p}=\lVert u \rVert_{L^{p}}$ ...
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### Extend the Fourier transform over $L^2(\mathbb R^n)$

Using Plancherel theorem, we have that the Fourier transform is an isometry over $L^2(\mathbb R^n)$. But anyway. In my course it's written that Plancherel theorem is extremely important since it allow ...
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### Irreducible representations of locally compact semigroups

What class of semigroups have finite dimensional irreducible representations. For example, If we have a compact groups $G$ then every continuous irreducible representation of $G$ is finite ...
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### Can you find shearlets in CNNs?

I read that you can find wavelets in the first layers of a CNN. Can you also find shearlets, and if not, why? Edit (further explanations): I read that, when you train a CNN the filters in the first ...
Let $f(x) = (1+\|x\|)^{-\frac{1}{2}}$ for $x \in \mathbb{R}^n$. This is clear that $f\star g \notin \mathcal S$ where $\mathcal S$ is algebra of Schwartz functions on $\mathbb{R}^n$ and $g \in \... 0answers 42 views ### How to calculate this integral tends to zero? I've posted this before, but I was unable to solve this... Setting : U is a bounded Lipschitz domain in the complex plane Consider the following classical Dirichlet problem for the Laplace operator:... 1answer 49 views ### How much does the$L^p$norms say about a function? Let's say we have two positive, decreasing function$u$and$v$on$[0,+\infty)$, and we know that$\|u\|_{L^p}=\|v\|_{L^p}$for all$p\ge1$, can we say something about$u$and$v$? Do they have to be ... 0answers 68 views ### Representation of a real function through a Fourier Transformation I 'm trying to do some calculations regarding some differential equations and I came across an interesting way to express a real function through a double integral of the form:$f(x)=\frac{1}{\pi}\...
I am stuck on how to prove the statement "A continuous action of a compact group $G$ on a uniform space $X$ is equicontinuous." So, essentially we want to show that for every entourage $\alpha$ of \$...