# Questions tagged [almost-periodic-function]

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### Lower bound of infinite sum of shifts

This is an extension of https://mathoverflow.net/posts/452526. So, it appears that $\sin(xt)$ serves as a better lower bound instead of a linear equation, in fact the series appears to uniformly ...
• 410
1 vote
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### Bounds of periodic functions formed from infinite series of shifts

Recently, I have become quite obsessed with the follow series: $$f(t,x)=\sum_{m=-\infty}^{\infty} (-1)^m f(t+x m)$$ where $f$ is analytic. This series automatically produces a periodic function with ...
• 410
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### Rotation number for multicomponent Schrödinger equation

Rotation number for Schrödinger equation of the form $$-x''(t) +q(t) x(t) = E x(t)$$ was defined in R. Johnson J. Moser "The rotation number for almost periodic ...
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### Does such a function exist?

I am looking for a function with the following property: Let $v_1,v_2$ be two linearly independent vectors in $\mathbb{R}^2.$ I am given a smooth function $g:(0,1) \rightarrow (0,\infty).$ I am trying ...
• 486
1 vote
90 views

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### C* algebras of Almost Periodic Functions

Suppose we take, for example, the $C^*$-algebra which is the sup norm closure of the exponentials $e^{2 \pi i ax}$ where $a \in \mathbb{Z} + \theta \mathbb{Z}$ for $\theta$ an irrational number. This ...
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### Besicovitch Almost Periodic Functions a subspace of what?

The common example of a nonseparable Hilbert space comes from the collection of Besicovitch almost periodic function spaces. Starting with $L^p_{\text{loc}}(\mathbb{R})$ we look at those elements ...
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