2020/07/23 by Asmahan Essa A Alajyan, A. E. Alajyan, Alajyan, A. E. +2
Engineering · Mathematics · #30H10 #30H20 #44A10 #46E15 #47N70 #93B36 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #math.CV #math.FA #math.OC #msc:30H10 #msc:30H20 #msc:44A10 #msc:46E15 #msc:47N70 #msc:93B36
paper · pdf · doi:10.48550/arxiv.2007.11871
12 pages, more motivation and background information added
openalex publication_date 2020/07/23 · arxiv created 2021/06/23 · arxiv updated 2021/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper extends the theory of Zen spaces (weighted Hardy/Berg\-man spaces on the right-hand half-plane) to the Hilbert-space valued case, and describes the multipliers on them; it is shown that the methods of H^∞ control can therefore be extended to a family of weighted L2 input and output spaces. Next, the particular case of retarded delay systems with operator-valued transfer functions is analysed, and the dependence of H^∞ structure on the delay is determined by developing an extension of the Walton--Marshall technique used in the scalar case. The method is illustrated with examples.