Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ. (2nd July 2012)

• Record Type: Journal Article
• Authors: Yuan, D. H.; Feng, Y.; Shen, Y. F.; Yang, S. Z.
• Other Names: Zelik Sergey V. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-07-02
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/746823
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We consider the multigenerator system { E m b l T n a l φ l, m, n ∈ ℤ, l = 0, …, r - 1 } for φ 0, …, φ r - 1 ∈ L 2 ( 𝕊 ) and a 0, b 0, …, a r - 1, b r - 1 > 0, where the parameters b 0, …, b r - 1 > 0 are not necessary the same. With the help of frame theory, we provide some sufficient or necessary conditions for the system to be a frame for L 2 ( 𝕊 ) . Moreover, we present some characterizations for this system to be a Parseval frame.