A remark about orthogonal polynomials

We suggest a renewal method for reconstructing a density in a special case by a system of polynomials orthogonal with respect to it.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 389–392, April, 1994.This work was partially supported by the Ukrainian State Committee on Science and Technology.     

A remark on spatial boundary value problems for hyperbolic equations

We derive sufficient conditions for the unique solvability of two boundary value problems for factorized hyperbolic equations.     

A remark on the mean curvature of a graph-like hypersurface in hyperbolic space

In this paper we investigate the mean curvature H of a radial graph in hyperbolic space Hn+1. We obtain an integral inequality for H, and find that the lower limit of H at infinity is less than or equal to 1 and the upper limit of H at infinity is more than or equal to −1. As a byproduct we get a relation between the n-dimensional volume of a bounded domain in an n-dimensional hyperbolic space and the (n−1)-dimensional volume of its boundary. We also sharpen the main result of a paper by P.-A. Nitsche dealing with the existence and uniqueness of graph-like prescribed mean curvature hypersurfaces in hyperbolic space.     

A probabilistic remark about the Abel-Goncharov interpolation problem

One considers probability distributions related to the Poisson distribution. It is shown that the boundary problems for the Poisson process admit an interpretation in terms of the well-known Abel-Goncharov interpolation problem.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 56, pp. 5–11, 1976.In conclusion the author expresses his gratitude to N. A. Sapogov for his interest in this paper.     

A remark about the Orlicz-Pettis theorem and the statistical convergence

In this paper we obtain a new version of the Orlicz-Pettis theorem by using statistical convergence. To obtain this result we prove a theorem of uniform convergence on matrices related to the statistical convergence.     

A remark about the density of the orbits of the Collatz permutation

In this work, we study the density of the orbits of the Collatz Permutation and discuss the long-standing problem of determining whether this permutation has only a finite number of distinct orbits.     

A remark about the interpolation of spaces of continuous, vector-valued functions

If A is a sectorial operator on a Banach space X, then the space C([0,1];(X,D(A))_θ,∞) is a subspace of the interpolation space (C([0,1];X),C([0,1];D(A)))_θ,∞. The inclusion is strict in general.     

Survival of the weak in hyperbolic spaces, a remark on competition and geometry

A simple competition model is presented. While in Euclidean spaces the weak will ``die out', in the presence of hyperbolicity, coexistence take place.