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Quasicrystals and Almost Periodicity [PDF]
Communications in Mathematical Physics, 2005 We introduce a topology ${\cal T}$ on the space $U$ of uniformly discrete subsets of the Euclidean space. Assume that $S$ in $U$ admits a unique autocorrelation measure. The diffraction measure of $S$ is purely atomic if and only if $S$ is almost periodic in $(U,{\cal T})$. This result relates idealized quasicrystals to almost periodicity.
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Almost periodicity in semiflows [PDF]
Proceedings of the American Mathematical Society, 1995 For a semiflow on a complete metric space we show that if a semiorbit has compact closure and its positive limit set consists of stable points, the orbit is asymptotically almost periodic. Under stronger hypotheses which are more tractable in applications, the same conclusion holds. An application to a scalar delay-differential equation is given.
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A simple almost-periodicity criterion and applications [PDF]
, 1987 We introduce a new almost-periodicity criterion for functions: R → X with X a complete metric space. This result is used to establish asymptotic almost periodicity of precompact positive trajectories to some differential equations of the form dudt + A(t)
Haraux, A, A Haraux
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Almost periodicity and periodicity for nonautonomous random dynamical systems
, 2020 International audienceWe present a notion of almost periodicity wich can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations).
Raynaud de Fitte, Paul
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Theoretical Computer Science, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrei A. Muchnik +2 more
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Almost Periodic Time Scales and Almost Periodic Functions on Time Scales [PDF]
Journal of Applied Mathematics, 2015 We propose some new concepts of almost periodic time scales and almost periodic functions on time scales and give some basic properties of these new types of almost periodic time scales and almost periodic functions on time scales. We also give some comments on a recent paper by Wang and Agarwal (2014) concerning a new almost periodic time scale.
Li, Yongkun, Li, Bing
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Cocycles and Almost Periodicity [PDF]
Journal of the London Mathematical Society, 1987 Let G be a compact abelian group containing, as a dense subgroup, the image of \({\mathbb{R}}\) by a continuous injective homomorphism, say \(\alpha\). A cocycle on G is defined here as a unitary \((=\) of modulus 1) continuous function on \(G\times {\mathbb{R}}\) satisfying the identity \(Y(g,s+t)=Y(g,s)Y(g+\alpha (s),t)\). A cocycle is called trivial
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Electronic Journal of Qualitative Theory of Differential Equations, 2008 The paper studies the notion of Stepanov almost periodicity (or $S^2$-almost periodicity) for stochastic processes, which is weaker than the notion of quadratic-mean almost periodicity.
P. Bezandry, Toka Diagana
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Almost Periodic Functions [PDF]
Proceedings of the American Mathematical Society, 1952 One of the aims in the study of almost periodic functions on a group is to generalize the Fejer summation process, whereby the Fourier series may be summed to yield the function. This has been achieved partially by Bochner-von Neumann [1] and Maak [2; 3].J But in [3] Maak says "In general it is not possible to give a summation procedure which may be ...
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Generalized Almost Periodicity in Measure
MathematicsThis paper investigates diverse classes of multidimensional Weyl and Doss ρ-almost periodic functions in a general measure setting. This study establishes the fundamental structural properties of these generalized ρ-almost periodic functions, extending ...
Marko Kostić +3 more
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