2021/12/29 by Stevan Pilipović, Pilipović, Stevan, Bojan Prangoski +1
Mathematics · #35S05 #46E35 #46F05 #47G30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2112.14461
openalex publication_date 2021/12/29 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We characterise the Weyl-Hörmander symbol classes S(M,g) via the growth of the action of the corresponding ΨDOs on time-frequency shifts of a single test function. For this purpose, we introduce a geometric short-time Fourier transform which is well-suited for the analysis of S(M,g). We define new modulation spaces and achieve the characterisation of the Weyl-Hörmander classes by showing that they are intersections of such modulation spaces suitable for the time-frequency characterisation.