On basicity of exponential and trigonometric systems in grand Lebesgue spaces

Creative Commons License

Ismailov M. I., ZEREN Y., Acar K. S., 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, PIECEWISE-LINEAR PHASE, APPROXIMATION, THEOREMS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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).