On basicity of exponential and trigonometric systems in grand Lebesgue spaces
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.51, sa.6, ss.1577-1587, 2022 (SCI-Expanded, Scopus, TRDizin)
- 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
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- 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).