2022/07/31 by Weichao Guo, Guo, Weichao, Guoping Zhao +1
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2208.00340
openalex publication_date 2022/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inspired by a recent article \cite[JFAA, 28(2):1-34, (2022)]Skrettingland2022JoFAaA, this paper is devoted to the study of suitable window class in the framework of bounded linear operators on L2(\rd). We establish a natural and complete characterization for the window class such that the corresponding STFT leads to equivalent norms of modulation spaces. The positive bounded linear operators are also characterized in Cohen's class distributions such that the corresponding quantities form equivalent norms of modulation spaces. As a generalization, we introduce a family of operator classes corresponding to the operator-valued modulation spaces. Some applications of our main theorems to the localization operators are also concerned.