Generalized Logan’s Problem for Entire Functions of Exponential Type and Optimal Argument in Jackson’s Inequality in L2（R3）  

作　　者：Valerii IVANOV Alexey IVANOV 

机构地区：[1]Department of Applied Mathematics and Computer Science,Tula State University

出　　处：《Acta Mathematica Sinica,English Series》2018年第10期1563-1577,共15页数学学报（英文版）

基　　金：Supported by the Russian Foundation for Basic Research(Grant No.16-01-00308)

摘　　要：We study Jackson＇s inequality between the best approximation of a function f∈ L2（R^3） by entire functions of exponential spherical type and its generalized modulus of continuity. We prove Jackson＇s inequality with the exact constant and the optimal argument in the modulus of continuity. In particular, Jackson＇s inequality with the optimal parameters is obtained for classical modulus of continuity of order r and Thue-Morse modulus of continuity of order r∈ N. These results are based on the solution of the generalized Logan problem for entire functions of exponential type. For it we construct a new quadrature formulas for entire functions of exponential type.We study Jackson＇s inequality between the best approximation of a function f∈ L2（R^3） by entire functions of exponential spherical type and its generalized modulus of continuity. We prove Jackson＇s inequality with the exact constant and the optimal argument in the modulus of continuity. In particular, Jackson＇s inequality with the optimal parameters is obtained for classical modulus of continuity of order r and Thue-Morse modulus of continuity of order r∈ N. These results are based on the solution of the generalized Logan problem for entire functions of exponential type. For it we construct a new quadrature formulas for entire functions of exponential type.

关 键 词：Best approximation generalized modulus of continuity Jackson＇s inequality optimal argument Logan＇s problem quadrature formula 

分 类 号：O174[理学—数学] O171[理学—基础数学]