Admissible Vectors of a Covariant Representation of a Dynamical System

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to a uniform lattice of $G$

Generated topology on infinite sets by ultrafilters

Let $X$ be an infinite set, equipped with a topology $tau$. In this paper we studied the relationship between $tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts

On the inclusions of XΦX^\Phi spaces

summary:We give some equivalent conditions (independent from the Young functions) for inclusions between some classes of $X^\Phi$ spaces, where $\Phi$ is a Young function and $X$ is a quasi-Banach function space on a $\sigma$-finite measure space $(\Omega ,\mathcal {A},\mu )$

On the inclusions of XΦX^\Phi spaces

We give some equivalent conditions (independent from the Young functions) for inclusions between some classes of $X^\Phi$ spaces, where $\Phi$ is a Young function and $X$ is a quasi-Banach function space on a $\sigma$-finite measure space $(\Omega,\mathcal{A},\mu)$