The main purpose of this paper is to investigate almost periodic properties of various classes of (a, k)-regularized C-resolvent families in Banach spaces. We contemplate the work of many other authors working in this field, giving also some original contributions and applications. In general case, (a, k)regularized C-resolvent families under our considerations are degenerate and their subgener...

We study the asymptotic behavior of large data solutions in the energy space H := H(R) in very high dimension d ≥ 11 to defocusing Schrödinger equations iut + ∆u = |u| u + V u in R, where V ∈ C∞ 0 (R ) is a real potential (which could contain bound states), and 1 + 4 d < p < 1 + 4 d−2 is an exponent which is energy-subcritical and mass-supercritical. In the spherically symmetric case, we show t...

The purpose of this article is to investigate the existence of almost periodic solutions of a system of almost periodic Lotka-Volterra difference equations which are a prey-predator system x1 n 1 x1 n exp{b1 n −a1 n x1 n −c2 n ∑n s −∞ K2 n−s x2 s }, x2 n 1 x2 n exp{−b2 n − a2 n x2 n c1 n ∑n s −∞ K1 n − s x1 s } and a competitive system xi n 1 xi n exp{bi n − aiixi n − ∑l j 1,j / i ∑n s −∞ Kij n...

In this paper, we study the existence of asymptotically almost periodic solutions to some classes of second-order partial functionaldifferential equations with unbounded delay. Our results are, subsequently, applied to studying the existence of asymptotically almost periodic solutions to some integrodifferential equations, which arise in the theory of heat conduction within fading memory materi...

Non blow-up of the 3D incompressible Euler Equations is proven for a class of threedimensional initial data characterized by uniformly large vorticity in bounded cylindrical domains. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to some 2D manifold. The approach of proving regularity is based on investigation of fast singu...

In this note we consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in R or Z. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally co...

We introduce a topology 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,T ). This result relates idealized quasicrystals to almost periodicity. In the context of ergodic point processes, the autocorrelation measure is known to...

A filter F on a group G is a T -filter if there is a Hausdorff group topology τ on G such that F τ −→ 0. This notion can be specialized for sequences, in which case we say that {an} is a T -sequence. In this paper, T -filters and T -sequences are studied. We characterize T -filters in non-abelian groups, show that certain filters can be interpreted as topological extensions of the notion of ker...

We develop a theory of almost periodic elements in Banach algebras and present an abstract version of a noncommutative Wiener’s Lemma. The theory can be used, for example, to derive some of the recently obtained results in time-frequency analysis such as the spectral properties of the finite linear combinations of time-frequency shifts.

We exhibit almost periodic potentials such that the corresponding SchrGdinger operators in the space of all square Haar-integrable functions on the Bohr compac-tilication of Iw have a point in the spectrum which is not an eigenvalue.