On basicity of exponential and trigonometric systems in grand Lebesgue spaces


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Ismailov M. I., ZEREN Y., Acar K. S., Aliyarova I. F.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.51, no.6, pp.1577-1587, 2022 (SCI-Expanded) identifier identifier

  • 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
  • Page Numbers: pp.1577-1587
  • Keywords: grand Lebesgue space, exponential system, minimality, density, basis, PIECEWISE-LINEAR PHASE, APPROXIMATION, THEOREMS
  • 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).