To the theory of Hilbert space’s unconditional basis from values of entire vector-functions
Journal Title: Дослідження в математиці і механіці - Year 2016, Vol 21, Issue 1
Abstract
Classes of entire functions of exponential type are considered in the article. They fulfil certain conditions related to theorems about unconditional basises from the values of entire vectorfunctions. In particular, for any (𝐴2)-weight 𝑤2 on R is given by entire function 𝜙 with zeros in region Im 𝑧 < 0; futher, for any 𝜀 > 0 the weight |𝑤−1+ (𝑥 + 𝑖𝜀)𝜙(𝑥 + 𝑖𝜀)|2 meets the 𝐴2-condition. Here 𝑤+ is an exterior function in region Im 𝑧 > 0 with a property that |𝑤+(𝑥 + 𝑖0)|2 = 𝑤2(𝑥) almost everywhere on R.
Authors and Affiliations
E. I. Olefir
Keywords
Related Articles
- EP ID EP190753
- DOI -
- Views 96
- Downloads 0
Split of gas stream onto the bubbles inside liquid
A theory of the approximate description of the splitting of the thin jat of ideal gas flowing into the incompressible frictionless liquid is constructed on the base of the balance equations of mass and energy. Under the...
On a two-step algorithm in structural and parametric optimization problems of linear control systems.
This paper deals with applying of a two-step optimization algorithm for structural and parametric optimization problems of linear control systems with fixed and floating switching points.
THE CRITERION FOR SOLVABILITY OF A LINEAR NOETHER’S BOUNDARY VALUE PROBLEM FOR A SYSTEM OF DYNAMICAL EQUATIONS ON A TIME SCALE
On a time scale, the linear Noether’s boundary value problem for a system of second-order dynamical equations is considered. This boundary-value problem is considered in the case when the operator of the linear part is i...
Asymptotic of rapid varying solutions of differential equations of the second order with rapid varying nonlinearities
The question of the asymptotic behavior of the differential equations’ solution by 𝑡 ↑ 𝜔 𝑦′′ = 𝛼0𝑝(𝑡)𝜙(𝑦), where 𝛼0 ∈ {−1, 1}, 𝑝 : [𝑎, 𝜔[−→]0,+∞[ is a continuous function, −∞ < 𝑎 < 𝜔 6 +∞ , 𝜙 : Δ𝑦0 −→]0,+∞[ is a twice co...
One generalization of the classical orthogonal polynomials
The differential equation of the second order, generalizing the differential equations leaded to Jacobi, Laguerre and Hermite polynomials, is considered in the paper. The orthogonality of the polynomials, which are the s...