2012/04/05 by Asghar Rahimi, Rahimi, Asghar, Abolhassan Fereydooni +1
Computer Science · Mathematics · #42C15 (Primary) 41A58 #47A58 (Secondary) #Digital Filter Design and Implementation #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #math.FA #msc:41A58 #msc:42C15 #msc:47A58
paper · pdf · doi:10.48550/arxiv.1204.1359
15 pages
arxiv created 2012/04/05 · openalex publication_date 2012/04/05 · arxiv updated 2012/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence (called the symbol) and synthesis. Weighted and controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator Also g-frames are the most popular generalization of frames that include almost all of the frame extensions. In this manuscript the concept of the controlled g-frames will be defined and we will show that controlled g-frames are equivalent to g-frames and so the controlled operators C and C0 can be used as preconditions in applications. Also the multiplier operator for this family of operators will be introduced and some of its properties will be shown.