On basicity of exponential and trigonometric systems in grand Lebesgue spaces

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

Hacettepe Journal of Mathematics and Statistics, cilt.51, sa.6, ss.1577-1587, 2022 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 6
  • Basım Tarihi: 2022
  • Doi Numarası: 10.15672/hujms.1076849
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1577-1587
  • Anahtar Kelimeler: grand Lebesgue space, exponential system, minimality, density, basis
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

Basis properties of exponential and trigonometric systems in grand Lebesgue spaces Lp)(−π, π) are studied. Based on a shift operator, we consider the subspace Gp)(−π, π) of the space Lp)(−π, π), 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∈Z for Gp)(−π, π) and the basicity of trigonometric systems {sin nt}n∈N and {cos nt}n∈N0 for Gp)(0, π).