Algebrability and nowhere Gevrey differentiability

被引：25

作者：

Bastin, F. ^{[1
]}

Conejero, J. A. ^{[2
]}

Esser, C. ^{[1
]}

Seoane-Sepulveda, J. B. ^{[3
]}

机构：

[1] Univ Liege, Inst Math B37, B-4000 Liege, Belgium

[2] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, E-46022 Valencia, Spain

[3] Univ Complutense Madrid, Dept Anal Matemat, Fac Matemat, E-28040 Madrid, Spain

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2015年 / 205卷 / 01期

关键词：

FUNCTION-SPACES; BANACH-SPACES; VECTOR-SPACES; SETS; SPACEABILITY; LINEABILITY; PREVALENCE; SUBSPACES; SUBSETS; EVERY;

D O I：

10.1007/s11856-014-1104-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that there exist c-generated algebras (and dense in C (a)([0, 1])) every nonzero element of which is a nowhere Gevrey differentiable function. This leads to results of dense algebrability (and, therefore, lineability) of functions enjoying this property. In the process of proving these results we also provide a new construction of nowhere Gevrey differentiable functions.

引用

页码：127 / 143

页数：17

共 31 条

[1] Lineability and spaceability of sets of functions on R [J].