In this work, we give a new variation of constants formula for some partial functional differential equations with infinite delay. We assume that the linear part is not necessarily densely defined and satisfies the known Hille-Yosida condition. When the phase space is a uniform fading memory space, we establish a spectral decomposition of the phase space. This allows us to study the existence o...

This paper is concerned with the influence of frequency modulation on the semiFredholm properties of Toeplitz operators with oscillating matrix symbols. The main results give conditions on an orientation-preserving homeomorphism α of the real line that ensure the following: if b belongs to a certain class of oscillating matrix functions (periodic, almost periodic, or semi-almost periodic matrix...

This paper is concerned with the study of weighted pseudo almost periodic mild solutions for semilinear boundary differential equations. Namely, some sufficient conditions for the existence and uniqueness of weighted pseudo almost periodic mild solutions of semilinear boundary differential equations are obtain.

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...

Using ergodicity of functions, we prove the existence and uniqueness of (asymptotically) almost periodic solution for some nonlinear differential equations. As a consequence, we generalize a Massera’s result. A counterexample is given to show that the ergodic condition cannot be dropped. 2000 Mathematics Subject Classification. Primary 34C27, 43A60, 37Axx, 28Dxx.

We prove that the error term Λ(R) in the Weyl asymptotic formula #{En ≤ R } = VolM 4π R + Λ(R), for the Laplace operator on a surface of revolution M satisfying a twist hypothesis, has the form Λ(R) = RF (R) where F (R) is an almost periodic function of the Besicovitch class B, and the Fourier series of F (R) in B is ∑ γ A(γ) cos(|γ|R− φ) where the sum goes over all closed geodesics on M , and ...

We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona type theorems, properties of divisors, holomorphic analogs of the Peter-Weyl approximation theorem, Hartogs type theorems, characterization of uniqueness sets. The model examples ...

This thesis consists of two papers devoted to the asymptotic analysis of eigenvalue problems in perforated domains. The first paper investigates by means of the two-scale convergence method the asymptotic behavior of eigenvalues and eigenfunctions of Stekloff eigenvalue problems in perforated domains. We prove a concise and precise homogenization result including convergence of gradients of eig...

Returning to a classical question in Harmonic Analysis we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers Z which is not in the norm-closure of the algebra B(Z) of Fourier-Stieltjes transforms of measures on the dual group Ẑ = T, and which is recurrent. We also show that there is a Polish monothetic group which is re...

We establish the following result. Theorem. Let α : G → L(X) be a σ(X, X∗) integrable bounded group representation whose Arveson spectrum Sp(α) is scattered. Then the subspace generated by all eigenvectors of the dual representation α∗ is w∗ dense in X∗. Moreover, the σ(X, X∗) closed subalgebra Wα generated by the operators αt (t ∈ G) is semisimple. If, in addition, X does not contain any copy ...