The present paper is devoted to the functions from a certain subclass of non-differentiable functions. The arguments and values of the considered functions are represented by the s-adic representation or the nega-s-adic ...

For s > 0, let H0 = (-∆)s be the fractional Laplacian. In this paper, we obtain Lieb-Thirring type inequalities for the fractional Schrödinger operator defined as H = H0 + V , where V ∈ Lp(ℝd), p ≥ 1, d ≥ 1, is a complex-valued ...

We prove a theorem which characterizes the Haar distribution on a compact Abelian group by the independence of n linear forms of n independent random variables. The coefficients of the forms are continuous endomorphisms ...

For a formal power series the conditions on the Gelfond-Leont'ev derivatives are found, under which the series represents a function, analytic in the disk {z : |z| < R}, 0 < R ≤ +∞.

An equation is obtained for the Stieltjes transform of the normalized distribution of singular values of non-symmetric band random matrices in the limit when the band width and rank of the matrix simultaneously tend to ...

There is given an example of probability distribution, not having Gaussian components, such that for any two independent identically distributed random variables ξ and η with this distribution and for all a ≠ 0, b ≠ 0 the ...

For a commutative system of nonselfadjoint unbounded operators A₁, A₂ the concept of colligation and associated open system is given. For these open systems, the consistency conditions are established and the conservation ...

We describe contraction properties on pro jective spaces for products of matrices governed by Markov chains which satisfy strong mixing conditions. Assuming that the subgroup generated by the corresponding matrices is ...

A perturbation of the Poisson equation by a biharmonic operator with a small multiplier ε is considered. The asymptotic behavior of the solution of the Dirichlet problem for this equation as ε → 0 is studied. The gradient ...

We consider the ensemble of real symmetric random matrices H(n,ρ) obtained from the determinant form of the Ihara zeta function of random graphs that have n vertices with the edge probability ρ/n. We prove that the normalized ...