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1 vote

Check an equation on the Heisenberg group $H_1$

First, the reference is: https://www.sciencedirect.com/science/article/pii/0022123682900787 Second, in the notation of the cited paper $H_n={\mathbb C}^n\times {\mathbb R}$. Hence, you must decide if ...
F Zaldivar's user avatar
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3 votes
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On compactly supported functions with prescribed sparse coordinates

This is a rather lazy version of an answer, but I will also indicate how I think a full answer can be produced. Let $u(x,z)$ be the solution of $-u''+qu=z u$ with $u(0,z)=0$, $u'(0,z)=1$. Then $$ B_L =...
Christian Remling's user avatar
1 vote

Fourier series but different waveform

Partial answer: About linear independence, it is true that if $f$ is non constant then the dilations $f_n(x)=f(nx), n\in \mathbb{N}$ are linearly independent. In fact suppose for a finite sum we ...
an_ordinary_mathematician's user avatar
4 votes
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A question about the maximal function

The answer is no. Let $m$ be a very large positive constant. You can find smooth $f$ that equals $m$ on a small ball $B_R(0)$ and still satisfy $\int_{B_6(0)}|f|<\delta$. You can do it with $R$ ...
Piotr Hajlasz's user avatar
0 votes

On self-duality of non-Archimedean local fields

Here is a general simple and self-contained proof for the self-duality of local fields, which in particular should answer the questions above. Let $k$ be any local field. Fix a non-trivial character $\...
Itamar Vigdorovich's user avatar

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