DIRECT THEOREMS IN THE THEORY OF APPROXIMATION OF VECTORS IN A BANACH SPACE WITH EXPONENTIAL TYPE ENTIRE VECTORS

被引：0

作者：

Grushka, Ya. ^{[1
]}

Torba, S. ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Math, 3 Tereshchenkivska, UA-01601 Kiev, Ukraine

来源：

METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY | 2007年 / 13卷 / 03期

关键词：

Direct and inverse theorems; modulo of continuity; Banach space; entire vectors of exponential type;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an arbitrary operator A on a Banach space X which is the generator of a C-0-group with certain growth condition at infinity, direct theorems on connection between the degree of smoothness of a vector x is an element of X with respect to the operator A, the rate of convergence to zero of the best approximation of x by exponential type entire vectors for the operator A, and the k-module of continuity are established. The results allow to obtain Jackson-type inequalities in a number of classic spaces of periodic functions and weighted L-p spaces.

引用

页码：267 / 278

页数：12