On basicity of exponential and trigonometric systems in grand Lebesgue spaces
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.51, no.6, pp.1577-1587, 2022 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 51 Issue: 6
- Publication Date: 2022
- Doi Number: 10.15672/hujms.1076849
- Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
- Page Numbers: pp.1577-1587
- Keywords: grand Lebesgue space, exponential system, minimality, density, basis, PIECEWISE-LINEAR PHASE, APPROXIMATION, THEOREMS
- Open Archive Collection: AVESIS Open Access Collection
- Yıldız Technical University Affiliated: Yes
Abstract
Basis properties of exponential and trigonometric systems in grand Lebesgue spaces Lp)(-7r, 7r) are studied. Based on a shift operator, we consider the subspace Gp)(-7r, 7r) of the space Lp)(-7r, 7r), where continuous functions are dense, and the boundedness of the singular operator in this subspace is proved. We establish the basicity of exponential system {eint}n is an element of Z for Gp)(-7r, 7r) and the basicity of trigonometric systems {sin nt}n is an element of N and {cos nt}n is an element of N0 for Gp)(0, 7r).