2016/01/04 by Jean-Marie Lescure, Lescure, Jean-Marie, Stéphane Vassout +1
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Operator Algebras (math.OA) #math.DG #math.OA
paper · pdf · doi:10.48550/arxiv.1601.00932
arxiv created 2016/01/04 · openalex publication_date 2016/01/04 · arxiv updated 2016/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As announced in [12], we develop a calculus of Fourier integral G-operators on any Lie groupoid G. For that purpose, we study convolability and invertibility of Lagrangian conic submanifolds of the symplectic groupoid T * G. We also identify those Lagrangian which correspond to equivariant families parametrized by the unit space G (0) of homogeneous canonical relations in (T * Gx 0) x (T * G x 0). This allows us to select a subclass of Lagrangian distributions on any Lie groupoid G that deserve the name of Fourier integral G-operators (G-FIO). By construction, the class of G-FIO contains the class of equivariant families of ordinary Fourier integral operators on the manifolds Gx, x ∈ G (0). We then develop for G-FIO the first stages of the calculus in the spirit of Hormander's work. Finally, we work out an example proving the efficiency of the present approach for studying Fourier integral operators on singular manifolds.