# 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 ...
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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 ...
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### Rotation number for multicomponent Schrödinger equation

Rotation number for Schrödinger equation of the form \begin{equation} -x''(t) +q(t) x(t) = E x(t) \end{equation} was defined in R. Johnson J. Moser "The rotation number for almost periodic ...
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I came across some meromorphic function, call it $f(z)$, which is "quasicrystalline" in the following sense: one can write $f$ as: $$f(z)=\frac{\sum_i a_i e^{i(q_{i,x}x+q_{i,y}y)}}{\sum_i ... 4 votes 1 answer 209 views ### Intuition for almost periodic solution and Poincaré recurrence theorem I would like to ask a question that I had asked yesterday on the site math.stackexchange and I still have not received an answer. Suppose that we have a PDE that admit a solution u that can be ... 1 vote 3 answers 231 views ### Can we calculate the probability that f(x) is positive for a random x\in(0,m) as m\to\infty? (uniform distribution) Following my previous question here, I have this function$$f(x)=10+3 \cos (ax-bx)+13 \cos (ax+bx)+2 \cos (\frac32 a x)+17 \cos (b x),$$with \frac ab \notin \mathbb{Q}. What is the limit$$ \lim_{m\... 226 views

### 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 ...
1 vote
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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 ...
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 ...