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The maximal ideal space of the set $AP(\mathbb R)$ of almost periodic functions. i.e the set of multiplicative linear functionals under the pointwise topology. …

Then $G$ is a nonelementary hyperbolic group with trivial maximal finite normal subgroup. … .; Sonkin, Dmitriy, Periodic quotients of hyperbolic and large groups., Groups Geom. Dyn. 3, No. 3, 423-452 (2009). …

Here we define the periodic autocorrelation as $$ C_a(\tau)=\sum_{t=0}^{n-1} a(t) a(t+\tau) $$ where the shift by $\tau$ is modulo $n.$ Jungnickel and Pott have a paper on perfect and almost perfect autocorrelation … Edit: As @MaxAlekseyev points out, Corollary 2.5 in the Jungnickel and Pott paper actually rules out the existence of a circulant matrix as desired by the OP for lengths $13<n\le 20201.$ Maximal length …

In QFT we have a Hilbert space $H_x$ at each point $x$ of space, or relativistically at each point of some maximal spacelike surface. … These all commute, and the C${}^*$-algebra they generate is just the algebra of almost periodic functions on $H$ acting as multiplication operators. …

the set of all speeds), we have $$ \Psi_{v_0}(t)=\sum_{v\in V} \psi(vt-v_0t)\ne 0\,. $$ This will mean that there is at least one runner in the interval of length $\delta$ ahead of every runner, so the maximal … Note now that for each $k\ne 0$, the mean value of $|F(kt)|^2$ (in the sense of almost-periodic functions, i.e., $\lim_{T\to\infty}\int_{-T}^T\dots\,dt$) is $n$, so the mean value of the sum under the …

(n\,times)...f(\xi))) \to 2\,\,\text{as}\,\, n \to \infty$$ Additionally, $A$ is connected and $2 \in A$, where further $A$ is the maximal of all sets to satisfy these properties. … Plus, least of all, it is linear almost everywhere. …

Does there exist a finite set of radii such that some aperiodic packing of the plane by disks of those radii is believed to achieve the maximal packing density (not achieved by any periodic packing)? … [Note to administrators: I wanted to add “aperiodic” or “quasicrystal” or something like that as a tag; I settled for “almost-periodic-function”, but please re-tag as appropriate.] …

The buzzword to look for is "maximally almost periodic". This is part of the theory of Bohr Compactifications. Start with a (locally compact) group $G$. … By definition, this means that $G$ is "maximally almost periodic" (MAP). …

The maximal open set $U$ with this property is called the basin of $f$. It is well known that every transitive Anosov diffeomorphism carries a unique SRB measure. … My solution : Let $p \in M$ be a periodic point associated to $\delta, S$ and $\{x, f(x),..., f^{n-1}(x)\}$ in the periodic exponential specification property. …

The decoupling theory also led to significant advances in dispersive PDEs and the construction of the first explicit almost $\Lambda(p)$ sets. … One of the great results in twentieth century Harmonic analysis is Carleson’s theorem that the Fourier series of an $L^2$ function converges almost everywhere and the slightly stronger results that maximal …

When will the cusps be dark (almost vertical slope)? When the edges are close to diameters. And when will that be? When $nx$ is close to $x+m/2$. … So we see $n-1$ maximally dark cusps (and likewise one can count the relatively darker cusps by cutting the circle in 3, 4 etc. and translate in terms of congruences). …

A continuous bounded function $f$ on $G$ is called (weakly) almost periodic if the set $L_Gf$ of left translates is relatively compact in the (weak) norm topology. … Then $f$ is uniformly continuous with respect to the left and right uniform structures on $G$ and all (weakly) almost periodic functions forms an abelian $C^*$-algebra with the norm of uniform convergence …

If $G$ is a Hausdorff topological group and $bG$ is its Bohr compactification, Wikipedia says that $G$ is called maximally almost periodic (MAP) if and only if the natural map $i : G \to bG$ is injective …

unfortunate, as $u$ is not a compactification in the sense usually used in topology, unless $G$ was compact to begin with (in fact, $u$ is rarely injective - groups for which $u$ is injective are called "maximally … almost periodic"). …

Note: I have restricted my answer to abelian $G$; $\iota$ can be defined for any topological group, but your question only makes sense when $\iota$ is injective, i.e. for “maximally almost-periodic” $G …