On Banach frameness of degenerate weighted exponential system

Ismailov M. I., ŞİMŞİR ACAR K.

Fixed Point Theory and Algorithms for Sciences and Engineering, cilt.2025, sa.1, 2025 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2025 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1186/s13663-025-00805-5
  • Dergi Adı: Fixed Point Theory and Algorithms for Sciences and Engineering
  • Derginin Tarandığı İndeksler: Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Basicity, Completeness, Frameness, Minimality, Muckenhoupt condition, Weighted exponential system
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

This work deals with the frameness of weighted exponential system E(ω,Z)={ω(t)eint}n∈Z in the space Lp(−π,π), p>1, with the weight function ω(t) of general form. Basis properties of E(ω,Z) in Lp(−π,π), p>1, are studied, in other words, the criteria of completeness, minimality and basicity of the system E(ω,Z) in the space Lp(−π,π), p>1, are given. Sufficient conditions for the completeness and minimality of E(ω,Z∖F) in Lp(−π,π), p>1, are found, where F is an arbitrary finite nonempty subset of the set of integers Z. A different method to prove that the system E(ω,Z∖F) does not form a Schauder basis for Lp(−π,π), p>1, is given. Theorem on a property of expansion system and criterion of Banach frameness for E(ω,Z) in Lp(−π,π), p>1, are proved. In particular, it is proved that the system E(ω,Z) with defect cannot form atomic decomposition for Lp(−π,π), p>1. The obtained results are the generalizations of those on the atomic decomposition of power weighted exponential system in Lp(−π,π), p>1, and the frameness of weighted exponential system in L2(−π,π).