Solving inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential one gets reflection coefficients s± and invertible operators I +Hs± , where Hs± is the Hankel operator related to the symbol s±. The Marchenko– Faddeev theorem (in the continuous case) [6] and the Guseinov theorem (in the discrete case) [4], guarantees the uniqueness of solution of the...

A theorem of Davis, Figiel, Johnson and Pe lczyński tells us that weakly-compact operators between Banach spaces factor through reflexive Banach spaces. The machinery underlying this result is that of the real interpolation method, which has been adapted to the category of operator spaces by Xu, showing the this factorisation result also holds for completely bounded weakly-compact maps. In this...

We prove results about the L-almost-periodicity of convolutions. One of these follows from a simple but rather general lemma about approximating a sum of functions in L, and gives a very short proof of a theorem of Green that if A and B are subsets of {1, . . . , N} of sizes αN and βN then A + B contains an arithmetic progression of length at least exp ( c(αβ logN) − log logN ) . Another almost...

Preface In his beautiful book [54], Jean Petitot proposes a subriemannian model for the primary visual cortex of mammals. This model is neurophysiologically justified. Further developments of this theory lead to efficient algorithms for image reconstruction , based upon the consideration of an associated hypoelliptic diffusion. The subriemannian model of Petitot (or certain of its improvements)...

Stability results for time-varying systems with output averaged using the norm are established. The discrete-time linear system is considered under a bound on time-average on the mean-value of the output norm. It is shown that under controllability, observability and a uniform bound on the matrix norm, the time-varying system is asymptotically and uniformly stable. If, in addition, the solution...

We characterize the weak almost periodicity of a vector-valued, bounded, continuous function. We show that if the range of the function is relatively weakly compact, then the relative weak compactness of its right orbit is equivalent to that of its left orbit. At the same time, we give the function some other equivalent properties. 1. Introduction. Let S be a semitopological semigroup, let ᐄ be...

In this paper, by using the contraction mapping principle and constructing a suitable Lyapunov functional, we established a set of easily applicable criteria for the existence, uniqueness and global attractivity of positive periodic solution and positive almost periodic solution of a neutral multi-species Logarithmic population model with multiple delays and impulses. The results improve and ge...

It is shown that, under two additional assumptions, uniformly weakly persistent semiflows are also uniformly strongly persistent even if they are non-autonomous. This result is applied to a time-heterogeneous model of S-I-R-S type for the spread of infectious childhood diseases. If some of the parameter functions are almost periodic, an almost sharp threshold result is obtained for uniform stro...

In this work we model and numerically analyse, the dynamics of a single species food-limited model with delay, we focus in the asymptotic behavior. We use the sub and supersolutions method to provide some numerical simulations of the asymptotic behavior for several cases, autonomous, periodic, almost periodic concluding with a model that incoporates nonlocal delays as well as a continuous delay...

Let (X, ‖ · ‖) be a Banach space, f : X → X continous Freche’t differentiable map.Denote the set of almost periodic point by A(f).In this paper,we prove that there exists an uncountable set Λ such that f |Λ is distributionally chaotic,and Λ ⊂ A(f).