The paper is devoted to discretization of integral norms functions from a given finite dimensional subspace. Even though this problem extremely important in applications, its systematic study has begun recently. In we obtain conditional theorem for all $L_q$, $1\le q<\infty$, which an extension known results $q=1$. To discretize the successfully, introduce new technique, combination probabilist...

On integrable discretization of the inhomogeneous Ablowitz-Ladik model. Abstract An integrable discretization of the inhomogeneous Ablowitz-Ladik model with a linear force is introduced. Conditions on parameters of the discretization which are necessary for reproducing Bloch oscillations are obtained. In particular, it is shown that the step of the discretization must be comensurable with the p...

We investigate how a C*-algebra could consist of functions on a noncommutative set: a discretization of a C*-algebra A is a ∗-homomorphism A → M that factors through the canonical inclusion C(X) ⊆ `∞(X) when restricted to a commutative C*-subalgebra. Any C*-algebra admits an injective but nonfunctorial discretization, as well as a possibly noninjective functorial discretization, where M is a C*...