квадратурная формула

Embeddings of Generalized Bounded Variation Function Spaces into Spaces of Functions with Given Majorant of Average Modulus of Continuity

Authors: Volosivets S. S., Vezhlev A. E.

In the present paper we study embeddings of some spaces of functions of generalized bounded variation into classes of functions with given majorant of average modulus of continuity introduced by B. Sendov and V. Popov. We consider the spaces ΛBV (p) of functions of bounded (Λ − p)-variation suggested by D. Waterman (for p = 1) and M. Shiba (for p > 1) and spaces V (v(n)) of functions with given majorant of its modulus of variation. The last quantity was introduced by Z. A. Chanturia. The necessary and sufficient conditions of such embeddings are proved.

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.