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 ...

In this work, since the importance of investigation oscillators solutions, an methodology for proving existence and stability almost anti-periodic solutions inertial neural networks model on time scales are discussed. By developing approach based differential inequality techniques coupled with Lyapunov function method. A numerical example is given illustration.

⎯ In this paper, the existence, uniqueness and global attractivity are discussed on almost periodic solution of SICNNs (shunting inhibitory cellular neural networks) with continuously distributed delays. By using the fixed point theorem, differential inequality technique and Lyapunov functional method, giving the new ranges of parameters, several sufficient conditions are obtained to ensure the...