экстремальная задача

On a Limit Value of a Remainder of the Lagrange Constant Corresponding to the Lagrange Trigonometrical Polynomial

Authors: Shakirov I. A.

The behavior of Lebesgue constant of a trigonometrical Lagrange polynomial interpolating the periodic function in an odd number of clusters is studied. The limit value of the remainder in the known asymptotic formula for this constant is found. A special representation of a remainder allowed us to establish its strict decreasing. On this basis, for a Lebesgue constant, a non-improvable uniform bilateral logarithmic function estimate is received.

On the Least Type of Entire Functions of Order ½ ∈ (0, 1) with Positive Zeros

Authors: Sherstyukova O. V.

The paper is devoted to the theory of extremal problems in classes of entire functions with constraints on the growth and distribution of zeros and is associated with problems of completeness of exponential systems in the complex domain. The question of finding the exact lower bound for types of all entire functions of order p ∈ (0, 1) whose zeros lie on the ray and have prescribed upper p-density and p-step is discussed. It is shown that the infimum is attained in this problem, and a detailed construction of the extremal function is given.