Starting from a general operator representation in the time-frequency domain, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A characterization of operators that can be realized as Gabor multipliers is given and necessary conditions for the existence of (Hilbert-Schmidt) optimal Gabor multiplier ap...

L is a continuous function from R× into X and f is a continuous function from R to X . The theory of functional differential equations with infinite delay has been developed by several authors. The fundamental task of that kind of equations is the choice of phase space . Since the history function t→ ut is not continuous in general if u : (−∞,T] → X is continuous (where T > 0). The paper [9] co...

Given two finite sets of integers S ⊆ N \ {0} and D ⊆ N \ {0, 1}, the impartial combinatorial game i-Mark(S,D) is played on a heap of tokens. From a heap of n tokens, each player can move either to a heap of n − s tokens for some s ∈ S, or to a heap of n/d tokens for some d ∈ D if d divides n. Such games can be considered as an integral variant of Mark-type games, introduced by Elwyn Berlekamp ...

Co-author: Lúıs Castro We will present a study of the Fredholm property for matrix Wiener-Hopf plus/minus Hankel operators with semi-almost periodic Fourier symbols. The Fredholm property will be described based on certain factorizations of the representatives at infinity of the original symbols, and on the geometrical mean values of the corresponding factors. The Fredholm indices of those oper...

In this paper, the averaging principle for quasi-geostrophic motions with rapidly oscillating forcing is proved, both on nite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and att...

The purpose of this paper is to introduce and study the notion of a vector-valued π-invariant mean associated to a unitary representation π of a locally compact groupG on S, a self-adjoint linear subspace containing I of B(Hπ). We obtain, among other results, an extension theorem for π-invariant completely positive maps and π-invariant means which characterizes amenability of G. We also study v...

We prove that one-dimensional Schrodinger operators with even almost periodic potential have no point spectrum for a dense Gδ in the hull. This implies purely singular continuous spectrum for the almost Mathieu equation for coupling larger than 2 and a dense Gδ in Θ even if the frequency is an irrational with good Diophantine properties.

Let {r(Z):Z>0} be a C0-semigroup on a Banach space X with generator A , and let x € X. If a (A) n ;'R is empty and t »-> T(t)x is uniformly continuous, then ||7"(Z)jc|| —> 0 as t —» oo . If the semigroup is sun-reflexive, o(A)CiiR is countable, Pa(A)DiS. is empty, and 1 >-> T(t)x is uniformly weakly continuous, then T(t)x —► 0 weakly as t —» oo . Questions of almost periodicity and of stabiliza...