On a Property of the Franklin System in C[0,1] and L1[0,1]

被引：0

作者：

Mikayelyan, V. G. ^{[1
]}

机构：

[1] Yerevan State Univ, Yerevan 375025, Armenia

来源：

MATHEMATICAL NOTES | 2020年 / 107卷 / 1-2期

关键词：

Franklin system; bounded completeness; monotonically bounded completeness;

D O I：

10.1134/S0001434620010289

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A problem posed by J. R. Holub is solved. In particular, it is proved that if {(f) over tilde (n)} is the normalized Franklin system in L-1[0, 1], {a(n)} is a monotone sequence converging to zero, and supn is an element of N parallel to Sigma(n)(k=0) a(k)(f) over tildek parallel to|(1)<+infinity, then the series n-ary sumation Sigma(infinity)(n=0)a(n)(f) over tilde (n) converges in L-1[0, 1]. A similar result is also obtained for C[0, 1].

引用

页码：284 / 287

页数：4

共 12 条

[1]

Bochkarev S V, 1974, MAT SBORNIK, V95137, P3

[2]

BOCHKAREV SV, 1974, MATH USSR SB, V24, P1

[3]

Bockarev S. V., 1975, Anal. Math, V1, P249, DOI [10.1007/bf02333175, DOI 10.1007/BF02333175, 10.1007/BF02333175]

[4] PROPERTIES OF ORTHONORMAL FRANKLIN SYSTEM .2. [J].