The formation and portraits of subspace Fa-frames. Issue 9 (13th June 2022)

• Record Type: Journal Article
• Authors: Li, Yun-Zhang; Hussain, Tufail
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 9(2022)
• Page Start: 1610
• Page End: 1630
• Publication Date: 2022-06-13
• Subjects: Frame -- Fa-frame -- subspace Fa-frame; 42C15 -- 42C40; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2020.1769014
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : In practice, the time variable cannot be negative. The square integrable function space L 2 ( R + ) defined on the half real line R + = ( 0, ∞ ) models the causal signal space. Given a >1, this paper addresses F a -frames in the setting of subspaces of L 2 ( R + ) . We establish the connection between subspace F a -frames and orthogonal projections; characterize all bounded linear operators on L 2 ( Z × T a ) that transform F a -frames into other F a -frames for a subspace V of L 2 ( R + ) ; and obtain some sufficient conditions for constructing F a -frames for V from an arbitrarily given one.